Basic Technical Mathematics with Calculus (11th Edition)
Basic Technical Mathematics with Calculus (11th Edition)
11th Edition
ISBN: 9780134437736
Author: Allyn J. Washington, Richard Evans
Publisher: PEARSON
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 23.3, Problem 26E
To determine

The derivative of the function y=9x−x3 and hence, to evaluate it at the point (2,10).

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Chapter 23 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 23.1 - Determine the continuity of the function . Ch. 23.1 - Prob. 2PECh. 23.1 - Find . Ch. 23.1 - Find . Ch. 23.1 - Prob. 1ECh. 23.1 - Prob. 2ECh. 23.1 - Prob. 3ECh. 23.1 - Prob. 4ECh. 23.1 - Prob. 5ECh. 23.1 - Prob. 6E
Ch. 23.1 - Prob. 7ECh. 23.1 - Prob. 8ECh. 23.1 - Prob. 9ECh. 23.1 - Prob. 10ECh. 23.1 - Prob. 11ECh. 23.1 - Prob. 12ECh. 23.1 - Prob. 13ECh. 23.1 - Prob. 14ECh. 23.1 - Prob. 15ECh. 23.1 - Prob. 16ECh. 23.1 - Prob. 17ECh. 23.1 - Prob. 18ECh. 23.1 - Prob. 19ECh. 23.1 - Prob. 20ECh. 23.1 - In Exercises 21–24, graph the function and...Ch. 23.1 - Prob. 22ECh. 23.1 - Prob. 23ECh. 23.1 - Prob. 24ECh. 23.1 - Prob. 25ECh. 23.1 - Prob. 26ECh. 23.1 - Prob. 27ECh. 23.1 - Prob. 28ECh. 23.1 - Prob. 29ECh. 23.1 - Prob. 30ECh. 23.1 - Prob. 31ECh. 23.1 - Prob. 32ECh. 23.1 - Prob. 33ECh. 23.1 - Prob. 34ECh. 23.1 - Prob. 35ECh. 23.1 - Prob. 36ECh. 23.1 - Prob. 37ECh. 23.1 - Prob. 38ECh. 23.1 - Prob. 39ECh. 23.1 - Prob. 40ECh. 23.1 - Prob. 41ECh. 23.1 - Prob. 42ECh. 23.1 - Prob. 43ECh. 23.1 - Prob. 44ECh. 23.1 - Prob. 45ECh. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - In Exercises 31–50, evaluate the indicated limits...Ch. 23.1 - Prob. 48ECh. 23.1 - Prob. 49ECh. 23.1 - Prob. 50ECh. 23.1 - Prob. 51ECh. 23.1 - Prob. 52ECh. 23.1 - Prob. 53ECh. 23.1 - Prob. 54ECh. 23.1 - Prob. 55ECh. 23.1 - Prob. 56ECh. 23.1 - Prob. 57ECh. 23.1 - Prob. 58ECh. 23.1 - Prob. 59ECh. 23.1 - A 5-Ω resistor and a variable resistor of...Ch. 23.1 - Prob. 61ECh. 23.1 - Prob. 62ECh. 23.1 - Prob. 63ECh. 23.1 - Prob. 64ECh. 23.1 - Prob. 65ECh. 23.1 - Prob. 66ECh. 23.1 - Prob. 67ECh. 23.1 - Prob. 68ECh. 23.1 - Prob. 69ECh. 23.1 - Prob. 70ECh. 23.1 - Prob. 71ECh. 23.1 - Prob. 72ECh. 23.2 - Find the slope of a line tangent to the curve of y...Ch. 23.2 - Prob. 2PECh. 23.2 - Prob. 1ECh. 23.2 - Prob. 2ECh. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - In Exercises 3–6, use the method of Example 1 to...Ch. 23.2 - Prob. 5ECh. 23.2 - Prob. 6ECh. 23.2 - In Exercises 7–10, use the method of Example 2 to...Ch. 23.2 - Prob. 8ECh. 23.2 - Prob. 9ECh. 23.2 - Prob. 10ECh. 23.2 - Prob. 11ECh. 23.2 - Prob. 12ECh. 23.2 - Prob. 13ECh. 23.2 - Prob. 14ECh. 23.2 - Prob. 15ECh. 23.2 - Prob. 16ECh. 23.2 - Prob. 17ECh. 23.2 - Prob. 18ECh. 23.2 - Prob. 19ECh. 23.2 - Prob. 20ECh. 23.2 - Prob. 21ECh. 23.2 - Prob. 22ECh. 23.2 - Prob. 23ECh. 23.2 - Prob. 24ECh. 23.2 - Prob. 25ECh. 23.2 - Prob. 26ECh. 23.2 - In Exercises 27–30, find the point(s) where the...Ch. 23.2 - Prob. 28ECh. 23.2 - Prob. 29ECh. 23.2 - Prob. 30ECh. 23.2 - Prob. 31ECh. 23.2 - Prob. 32ECh. 23.2 - Prob. 33ECh. 23.2 - Prob. 34ECh. 23.3 - Using the definiton, find the derivative of y = 5x...Ch. 23.3 - Prob. 2PECh. 23.3 - Prob. 1ECh. 23.3 - Prob. 2ECh. 23.3 - Prob. 3ECh. 23.3 - Prob. 4ECh. 23.3 - Prob. 5ECh. 23.3 - Prob. 6ECh. 23.3 - Prob. 7ECh. 23.3 - Prob. 8ECh. 23.3 - Prob. 9ECh. 23.3 - Prob. 10ECh. 23.3 - Prob. 11ECh. 23.3 - Prob. 12ECh. 23.3 - Prob. 13ECh. 23.3 - Prob. 14ECh. 23.3 - Prob. 15ECh. 23.3 - Prob. 16ECh. 23.3 - Prob. 17ECh. 23.3 - Prob. 18ECh. 23.3 - Prob. 19ECh. 23.3 - Prob. 20ECh. 23.3 - Prob. 21ECh. 23.3 - Prob. 22ECh. 23.3 - Prob. 23ECh. 23.3 - Prob. 24ECh. 23.3 - In Exercises 25–28, find the derivative of each...Ch. 23.3 - Prob. 26ECh. 23.3 - Prob. 27ECh. 23.3 - Prob. 28ECh. 23.3 - Prob. 29ECh. 23.3 - Prob. 30ECh. 23.3 - Prob. 31ECh. 23.3 - Prob. 32ECh. 23.3 - Prob. 33ECh. 23.3 - Prob. 34ECh. 23.3 - Prob. 35ECh. 23.3 - Prob. 36ECh. 23.3 - Prob. 37ECh. 23.3 - Prob. 38ECh. 23.3 - Prob. 39ECh. 23.3 - Prob. 40ECh. 23.4 - Prob. 1PECh. 23.4 - Prob. 2PECh. 23.4 - Prob. 1ECh. 23.4 - Prob. 2ECh. 23.4 - Prob. 3ECh. 23.4 - Prob. 4ECh. 23.4 - Prob. 5ECh. 23.4 - Prob. 6ECh. 23.4 - Prob. 7ECh. 23.4 - Prob. 8ECh. 23.4 - Prob. 9ECh. 23.4 - Prob. 10ECh. 23.4 - Prob. 11ECh. 23.4 - Prob. 12ECh. 23.4 - Prob. 13ECh. 23.4 - Prob. 14ECh. 23.4 - Prob. 15ECh. 23.4 - Prob. 16ECh. 23.4 - Prob. 17ECh. 23.4 - Prob. 18ECh. 23.4 - Prob. 19ECh. 23.4 - Prob. 20ECh. 23.4 - Prob. 21ECh. 23.4 - Prob. 22ECh. 23.4 - Prob. 23ECh. 23.4 - Prob. 24ECh. 23.4 - Prob. 25ECh. 23.4 - Prob. 26ECh. 23.4 - Prob. 27ECh. 23.4 - Prob. 28ECh. 23.4 - Prob. 29ECh. 23.4 - Prob. 30ECh. 23.4 - Prob. 31ECh. 23.4 - Prob. 32ECh. 23.4 - Prob. 33ECh. 23.4 - Prob. 34ECh. 23.4 - Prob. 35ECh. 23.4 - Prob. 36ECh. 23.4 - Prob. 37ECh. 23.4 - Prob. 38ECh. 23.4 - Prob. 39ECh. 23.4 - Prob. 40ECh. 23.4 - Prob. 41ECh. 23.4 - Prob. 42ECh. 23.4 - In Exercises 27–46, find the indicated...Ch. 23.4 - Prob. 44ECh. 23.4 - Prob. 45ECh. 23.4 - Prob. 46ECh. 23.5 - Prob. 1PECh. 23.5 - Prob. 2PECh. 23.5 - Prob. 1ECh. 23.5 - Prob. 2ECh. 23.5 - Prob. 3ECh. 23.5 - Prob. 4ECh. 23.5 - Prob. 5ECh. 23.5 - Prob. 6ECh. 23.5 - Prob. 7ECh. 23.5 - Prob. 8ECh. 23.5 - Prob. 9ECh. 23.5 - Prob. 10ECh. 23.5 - Prob. 11ECh. 23.5 - In Exercises 5–20, find the derivative of each of...Ch. 23.5 - Prob. 13ECh. 23.5 - Prob. 14ECh. 23.5 - Prob. 15ECh. 23.5 - Prob. 16ECh. 23.5 - Prob. 17ECh. 23.5 - Prob. 18ECh. 23.5 - Prob. 19ECh. 23.5 - Prob. 20ECh. 23.5 - Prob. 21ECh. 23.5 - Prob. 22ECh. 23.5 - Prob. 23ECh. 23.5 - Prob. 24ECh. 23.5 - Prob. 25ECh. 23.5 - Prob. 26ECh. 23.5 - Prob. 27ECh. 23.5 - Prob. 28ECh. 23.5 - Prob. 29ECh. 23.5 - Prob. 30ECh. 23.5 - Prob. 31ECh. 23.5 - Prob. 32ECh. 23.5 - Prob. 33ECh. 23.5 - Prob. 34ECh. 23.5 - Prob. 35ECh. 23.5 - Prob. 36ECh. 23.5 - Prob. 37ECh. 23.5 - Prob. 38ECh. 23.5 - Prob. 39ECh. 23.5 - Prob. 40ECh. 23.5 - Prob. 41ECh. 23.5 - Prob. 42ECh. 23.5 - Prob. 43ECh. 23.5 - Prob. 44ECh. 23.5 - Prob. 45ECh. 23.5 - Prob. 46ECh. 23.5 - Prob. 47ECh. 23.5 - Prob. 48ECh. 23.5 - Prob. 49ECh. 23.5 - Prob. 50ECh. 23.5 - Prob. 51ECh. 23.5 - Prob. 52ECh. 23.5 - Prob. 53ECh. 23.5 - Prob. 54ECh. 23.5 - Prob. 55ECh. 23.5 - Prob. 56ECh. 23.6 - Find the derivative of . Do not multiply factors...Ch. 23.6 - Prob. 2PECh. 23.6 - Prob. 1ECh. 23.6 - Prob. 2ECh. 23.6 - Prob. 3ECh. 23.6 - Prob. 4ECh. 23.6 - Prob. 5ECh. 23.6 - Prob. 6ECh. 23.6 - Prob. 7ECh. 23.6 - Prob. 8ECh. 23.6 - Prob. 9ECh. 23.6 - Prob. 10ECh. 23.6 - Prob. 11ECh. 23.6 - Prob. 12ECh. 23.6 - Prob. 13ECh. 23.6 - Prob. 14ECh. 23.6 - Prob. 15ECh. 23.6 - Prob. 16ECh. 23.6 - Prob. 17ECh. 23.6 - Prob. 18ECh. 23.6 - Prob. 19ECh. 23.6 - Prob. 20ECh. 23.6 - Prob. 21ECh. 23.6 - Prob. 22ECh. 23.6 - Prob. 23ECh. 23.6 - Prob. 24ECh. 23.6 - Prob. 25ECh. 23.6 - Prob. 26ECh. 23.6 - Prob. 27ECh. 23.6 - Prob. 28ECh. 23.6 - Prob. 29ECh. 23.6 - Prob. 30ECh. 23.6 - Prob. 31ECh. 23.6 - Prob. 32ECh. 23.6 - Prob. 33ECh. 23.6 - Prob. 34ECh. 23.6 - Prob. 35ECh. 23.6 - Prob. 36ECh. 23.6 - Prob. 37ECh. 23.6 - Prob. 38ECh. 23.6 - Prob. 39ECh. 23.6 - Prob. 40ECh. 23.6 - Prob. 41ECh. 23.6 - Prob. 42ECh. 23.6 - Prob. 43ECh. 23.6 - Prob. 44ECh. 23.6 - In Exercises 33–58, solve the given problems by...Ch. 23.6 - Prob. 46ECh. 23.6 - Prob. 47ECh. 23.6 - Prob. 48ECh. 23.6 - Prob. 49ECh. 23.6 - Prob. 50ECh. 23.6 - Prob. 51ECh. 23.6 - Prob. 52ECh. 23.6 - Prob. 53ECh. 23.6 - Prob. 54ECh. 23.6 - Prob. 55ECh. 23.6 - Prob. 56ECh. 23.6 - Prob. 57ECh. 23.6 - Prob. 58ECh. 23.7 - Prob. 1PECh. 23.7 - Prob. 2PECh. 23.7 - Prob. 3PECh. 23.7 - Prob. 4PECh. 23.7 - Prob. 1ECh. 23.7 - Prob. 2ECh. 23.7 - Prob. 3ECh. 23.7 - Prob. 4ECh. 23.7 - Prob. 5ECh. 23.7 - Prob. 6ECh. 23.7 - Prob. 7ECh. 23.7 - Prob. 8ECh. 23.7 - Prob. 9ECh. 23.7 - Prob. 10ECh. 23.7 - Prob. 11ECh. 23.7 - Prob. 12ECh. 23.7 - Prob. 13ECh. 23.7 - Prob. 14ECh. 23.7 - Prob. 15ECh. 23.7 - Prob. 16ECh. 23.7 - Prob. 17ECh. 23.7 - Prob. 18ECh. 23.7 - Prob. 19ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 21ECh. 23.7 - Prob. 22ECh. 23.7 - Prob. 23ECh. 23.7 - Prob. 24ECh. 23.7 - Prob. 25ECh. 23.7 - Prob. 26ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 28ECh. 23.7 - Prob. 29ECh. 23.7 - Prob. 30ECh. 23.7 - In Exercises 5–32, find the derivative of each of...Ch. 23.7 - Prob. 32ECh. 23.7 - Prob. 33ECh. 23.7 - Prob. 34ECh. 23.7 - Prob. 35ECh. 23.7 - Prob. 36ECh. 23.7 - Prob. 37ECh. 23.7 - Prob. 38ECh. 23.7 - Prob. 39ECh. 23.7 - Prob. 40ECh. 23.7 - Prob. 41ECh. 23.7 - Prob. 42ECh. 23.7 - Prob. 43ECh. 23.7 - Prob. 44ECh. 23.7 - Prob. 45ECh. 23.7 - Prob. 46ECh. 23.7 - Prob. 47ECh. 23.7 - Prob. 48ECh. 23.7 - Prob. 49ECh. 23.7 - Prob. 50ECh. 23.7 - Prob. 51ECh. 23.7 - Prob. 52ECh. 23.7 - Prob. 53ECh. 23.7 - Prob. 54ECh. 23.7 - Prob. 55ECh. 23.7 - Prob. 56ECh. 23.7 - Prob. 57ECh. 23.7 - Prob. 58ECh. 23.8 - Prob. 1PECh. 23.8 - Prob. 1ECh. 23.8 - Prob. 2ECh. 23.8 - In Exercises 3–22, find dy/dx by differentiating...Ch. 23.8 - Prob. 4ECh. 23.8 - Prob. 5ECh. 23.8 - Prob. 6ECh. 23.8 - Prob. 7ECh. 23.8 - Prob. 8ECh. 23.8 - Prob. 9ECh. 23.8 - Prob. 10ECh. 23.8 - Prob. 11ECh. 23.8 - Prob. 12ECh. 23.8 - Prob. 13ECh. 23.8 - Prob. 14ECh. 23.8 - Prob. 15ECh. 23.8 - Prob. 16ECh. 23.8 - Prob. 17ECh. 23.8 - Prob. 18ECh. 23.8 - Prob. 19ECh. 23.8 - Prob. 20ECh. 23.8 - Prob. 21ECh. 23.8 - Prob. 22ECh. 23.8 - Prob. 23ECh. 23.8 - Prob. 24ECh. 23.8 - Prob. 25ECh. 23.8 - Prob. 26ECh. 23.8 - Prob. 27ECh. 23.8 - Prob. 28ECh. 23.8 - Prob. 29ECh. 23.8 - Prob. 30ECh. 23.8 - Prob. 31ECh. 23.8 - Prob. 32ECh. 23.8 - Prob. 33ECh. 23.8 - Prob. 34ECh. 23.8 - Prob. 35ECh. 23.8 - Prob. 36ECh. 23.8 - Prob. 37ECh. 23.8 - Prob. 38ECh. 23.8 - Prob. 39ECh. 23.8 - Prob. 40ECh. 23.8 - Prob. 41ECh. 23.8 - Prob. 42ECh. 23.8 - Prob. 43ECh. 23.8 - Prob. 44ECh. 23.9 - Prob. 1PECh. 23.9 - Prob. 2PECh. 23.9 - Prob. 1ECh. 23.9 - Prob. 2ECh. 23.9 - Prob. 3ECh. 23.9 - Prob. 4ECh. 23.9 - Prob. 5ECh. 23.9 - Prob. 6ECh. 23.9 - Prob. 7ECh. 23.9 - Prob. 8ECh. 23.9 - Prob. 9ECh. 23.9 - Prob. 10ECh. 23.9 - Prob. 11ECh. 23.9 - Prob. 12ECh. 23.9 - Prob. 13ECh. 23.9 - Prob. 14ECh. 23.9 - Prob. 15ECh. 23.9 - Prob. 16ECh. 23.9 - Prob. 17ECh. 23.9 - Prob. 18ECh. 23.9 - Prob. 19ECh. 23.9 - Prob. 20ECh. 23.9 - Prob. 21ECh. 23.9 - Prob. 22ECh. 23.9 - Prob. 23ECh. 23.9 - Prob. 24ECh. 23.9 - Prob. 25ECh. 23.9 - Prob. 26ECh. 23.9 - Prob. 27ECh. 23.9 - Prob. 28ECh. 23.9 - Prob. 29ECh. 23.9 - Prob. 30ECh. 23.9 - Prob. 31ECh. 23.9 - Prob. 32ECh. 23.9 - Prob. 33ECh. 23.9 - Prob. 34ECh. 23.9 - Prob. 35ECh. 23.9 - Prob. 36ECh. 23.9 - Prob. 37ECh. 23.9 - Prob. 38ECh. 23.9 - Prob. 39ECh. 23.9 - Prob. 40ECh. 23.9 - Prob. 41ECh. 23.9 - Prob. 42ECh. 23.9 - Prob. 43ECh. 23.9 - Prob. 44ECh. 23.9 - Prob. 45ECh. 23.9 - Prob. 46ECh. 23.9 - Prob. 47ECh. 23.9 - Prob. 48ECh. 23.9 - Prob. 49ECh. 23.9 - Prob. 50ECh. 23.9 - Prob. 51ECh. 23.9 - Prob. 52ECh. 23 - Prob. 1RECh. 23 - Prob. 2RECh. 23 - Prob. 3RECh. 23 - Prob. 4RECh. 23 - Prob. 5RECh. 23 - Prob. 6RECh. 23 - Prob. 7RECh. 23 - Prob. 8RECh. 23 - Prob. 9RECh. 23 - Prob. 10RECh. 23 - Prob. 11RECh. 23 - Prob. 12RECh. 23 - Prob. 13RECh. 23 - Prob. 14RECh. 23 - Prob. 15RECh. 23 - Prob. 16RECh. 23 - Prob. 17RECh. 23 - Prob. 18RECh. 23 - Prob. 19RECh. 23 - Prob. 20RECh. 23 - In Exercises 21–28, use the definition to find the...Ch. 23 - Prob. 22RECh. 23 - Prob. 23RECh. 23 - Prob. 24RECh. 23 - Prob. 25RECh. 23 - Prob. 26RECh. 23 - Prob. 27RECh. 23 - Prob. 28RECh. 23 - Prob. 29RECh. 23 - Prob. 30RECh. 23 - Prob. 31RECh. 23 - Prob. 32RECh. 23 - Prob. 33RECh. 23 - Prob. 34RECh. 23 - Prob. 35RECh. 23 - Prob. 36RECh. 23 - Prob. 37RECh. 23 - Prob. 38RECh. 23 - Prob. 39RECh. 23 - Prob. 40RECh. 23 - Prob. 41RECh. 23 - Prob. 42RECh. 23 - Prob. 43RECh. 23 - Prob. 44RECh. 23 - Prob. 45RECh. 23 - Prob. 46RECh. 23 - Prob. 47RECh. 23 - Prob. 48RECh. 23 - Prob. 49RECh. 23 - Prob. 50RECh. 23 - Prob. 51RECh. 23 - Prob. 52RECh. 23 - Prob. 53RECh. 23 - Prob. 54RECh. 23 - Prob. 55RECh. 23 - Prob. 56RECh. 23 - Prob. 57RECh. 23 - Prob. 58RECh. 23 - Prob. 59RECh. 23 - Prob. 60RECh. 23 - Prob. 61RECh. 23 - Prob. 62RECh. 23 - Prob. 63RECh. 23 - Prob. 64RECh. 23 - If $5000 is invested at interest rate i,...Ch. 23 - The temperature T (in °C) of a rotating machine...Ch. 23 - Prob. 67RECh. 23 - Prob. 68RECh. 23 - Prob. 69RECh. 23 - Prob. 70RECh. 23 - Prob. 71RECh. 23 - Prob. 72RECh. 23 - Prob. 73RECh. 23 - Prob. 74RECh. 23 - Prob. 75RECh. 23 - Prob. 76RECh. 23 - Prob. 77RECh. 23 - Prob. 78RECh. 23 - Prob. 79RECh. 23 - Prob. 80RECh. 23 - Prob. 81RECh. 23 - Prob. 82RECh. 23 - Prob. 83RECh. 23 - Prob. 84RECh. 23 - Prob. 85RECh. 23 - Prob. 86RECh. 23 - Prob. 87RECh. 23 - Prob. 88RECh. 23 - Prob. 89RECh. 23 - Prob. 90RECh. 23 - Prob. 91RECh. 23 - Prob. 92RECh. 23 - Prob. 93RECh. 23 - Prob. 94RECh. 23 - Prob. 95RECh. 23 - Prob. 96RECh. 23 - Prob. 97RECh. 23 - Prob. 98RECh. 23 - In Exercises 53–98, solve the given problems. 99....Ch. 23 - Prob. 1PTCh. 23 - Prob. 2PTCh. 23 - Prob. 3PTCh. 23 - Prob. 4PTCh. 23 - Prob. 5PTCh. 23 - Prob. 6PTCh. 23 - Prob. 7PTCh. 23 - Prob. 8PTCh. 23 - Prob. 9PTCh. 23 - Prob. 10PT
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