4th Edition

ISBN: 9780135874738

Author: Sullivan

Publisher: PEARSON

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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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Textbook Question

Chapter 6, Problem 11CR

Consider the function

f ( x ) = 2 x 5 − x 4 − 4 x 3 + 2 x 2 + 2 x − 1

Find the real zeros and their multiplicity.

Find the intercepts.

Find the power function that the graph of f resembles for large | x | .

Graph f using a graphing utility.

Approximate the turning points, if any exist.

Use the information obtained in parts ( a ) − ( e ) to graph f by hand.

Identify the intervals on which f is increasing, decreasing, or constant.

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Chapter 6, Problem 10CR

Chapter 6, Problem 12CR

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Taylor Series Approximation Example- H.W More terms used implies better approximation f(x) 4 f(x) Zero order f(x + 1) = f(x;) First order f(x; + 1) = f(x;) + f'(x;)h 1.0 Second order 0.5 True f(x + 1) = f(x) + f'(x)h + ƒ"(x;) h2 2! f(x+1) 0 x; = 0 x+1 = 1 x h f(x)=0.1x4-0.15x³- 0.5x2 -0.25x + 1.2 51 Taylor Series Approximation H.w: Smaller step size implies smaller error Errors f(x) + f(x,) Zero order f(x,+ 1) = f(x) First order 1.0 0.5 Reduced step size Second order True f(x + 1) = f(x) + f'(x)h f(x; + 1) = f(x) + f'(x)h + "(xi) h2 f(x,+1) O x₁ = 0 x+1=1 Using Taylor Series Expansion estimate f(1.35) with x0 =0.75 with 5 iterations (or & s= 5%) for f(x)=0.1x 0.15x³-0.5x²- 0.25x + 1.2 52

Could you explain this using the formula I attached and polar coorindates

Could you explain this using the formula I attached and polar coordinates

Chapter 6 Solutions

PRECALCULUS:CONCEPTS...-MYLAB+ETEXT

Ch. 6.1 - What is the domain and the range of y=sinx ? (p....Ch. 6.1 - A suitable restriction on the domain of the...Ch. 6.1 - tan4=;sin3=;sin(6)=;cos=.Ch. 6.1 - 4. True or False The graph of is decreasing on the...Ch. 6.1 - 5. Ch. 6.1 - sin(6)=______; cos= _____;Ch. 6.1 - y=sin1x Means_____, where 1x1 and 2y2.Ch. 6.1 - cos1(cosx)=x, where_____.Ch. 6.1 - 9. , where______; Ch. 6.1 - 10. True or False The domain of is .

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Solution Summary: The author explains that the real zeros of f(x) are 1 and 2, respectively.

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