(a) Let f be a function that is continuous everywhere and letf(x) sin²(x)if x + 0F(x) =0,otherwiseUse the definition of derivatives to evaluate F'(0).Your answer should bein terms of f.(b) Let f(x) = x² sin(÷) for x # 0, and f(0) = 0. Find f'(0) (or say why itdoesn't exist.)

Introduction: The necessary condition for a function to be differentiable is that the function must…

Answered: (a) Let f be a function that is…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.6: Analyzing Graphs Of Functions

Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

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3. Find the derivative of (a) f(x) = (x + 2 sin x) (1 – 6 cos x), and (b) g(x) = sin x/ 7x
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a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent line to the graph of f(x) = x2 - 5x at x = -1 and at x = 3.
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(a) Let f be a function that is continuous everywhere and let f(x) sin²(x), if x #0 0, otherwise F(x): = Use the definition of derivatives to evaluate F'(0). Your answer should be in terms of f. (b) Let f(x) = x² sin() for x = 0, and f(0) = 0. Find f'(0) (or say why it doesn't exist.)