Explanation Given: The function is defined for x ≠ 0 and is differentiable at all points except at x = 0 and x = 1 and that f ' ( x ) = 0 only at x = ± 2 Calculation: The critical points of the function, therefore will be x = − 2 ; x = 0 ; x = 1 ; x = 2 Therefore, the differentiation of the function will be f ' ( x )

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Chapter 3.1, Problem 6C

To determine

All the critical points and the graph of function f

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Chapter 3.1, Problem 5C

Chapter 3.1, Problem 7C

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The correct answer is D Could you explain and show the steps please

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

Chapter 3 Solutions

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All the critical points and the graph of function f

Solution Summary: The author explains that the function f is defined for xne 0 and is differentiable at all points except at X = 1 and that its graph can be drawn.

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All the critical points and the graph of function f

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Chapter 3 Solutions