To determine To find: The derivative f ( x ) = x 3 9 − 7 x 2 and the value of f ' ( 3 ) . Explanation Given: The function is f ( x ) = x 3 9 − 7 x 2 . Formula used: (1) The sum or difference rule , d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) . (2) The constant times of function, d d x ( k . g ( x ) ) = k . d d x ( g ( x ) ) . (3) The power rule, d d x ( x n ) = n x n − 1 . Calculation: The derivative f ' ( x ) of the given function is computed as follows, f ' ( x ) = d ( f ( x ) ) d x = d d x [ x 3 9 − 7 x 2 ] = d d x [ x 3 9 ] + d d x [ − 7 x 2 ] [ ∵ d d x ( u ( x ) + v ( x ) ) = d d x ( u ( x ) ) + d d x ( v ( x ) ) ] On further simplification, f ' ( x ) = 1 9 [ d d x ( x 3 ) ] − 7 [ d d x ( x 2 ) ] [ ∵ d d x ( k

11th Edition

ISBN: 9780133863369

Author: RITCHEY

Publisher: VST

See similar textbooks

Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Videos

Question

Chapter 4.1, Problem 30E

To determine

To find: The derivative f(x)=x39−7x2 and the value of f'(3) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.1, Problem 29E

Chapter 4.1, Problem 31E

Students have asked these similar questions

Consider the region below f(x) = (11-x), above the x-axis, and between x = 0 and x = 11. Let x; be the midpoint of the ith subinterval. Complete parts a. and b. below. a. Approximate the area of the region using eleven rectangles. Use the midpoints of each subinterval for the heights of the rectangles. The area is approximately square units. (Type an integer or decimal.)

Rama/Shutterstock.com Romaset/Shutterstock.com The power station has three different hydroelectric turbines, each with a known (and unique) power function that gives the amount of electric power generated as a function of the water flow arriving at the turbine. The incoming water can be apportioned in different volumes to each turbine, so the goal of this project is to determine how to distribute water among the turbines to give the maximum total energy production for any rate of flow. Using experimental evidence and Bernoulli's equation, the following quadratic models were determined for the power output of each turbine, along with the allowable flows of operation: 6 KW₁ = (-18.89 +0.1277Q1-4.08.10 Q) (170 - 1.6 · 10¯*Q) KW2 = (-24.51 +0.1358Q2-4.69-10 Q¹²) (170 — 1.6 · 10¯*Q) KW3 = (-27.02 +0.1380Q3 -3.84-10-5Q) (170 - 1.6-10-ºQ) where 250 Q1 <1110, 250 Q2 <1110, 250 <3 < 1225 Qi = flow through turbine i in cubic feet per second KW = power generated by turbine i in kilowatts

Hello! Please solve this practice problem step by step thanks!

Chapter 4 Solutions

EBK CALCULUS WITH APPLICATIONS, BRIEF V

Ch. 4.1 - YOUR TURN 1 find f′(t). Ch. 4.1 - YOUR TURN 2 find dy/dx. Ch. 4.1 - Prob. 3YT Ch. 4.1 - Prob. 4YT Ch. 4.1 - Prob. 5YT Ch. 4.1 - Prob. 1WE Ch. 4.1 - Prob. 2WE Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.