The right-sided and left-sided derivatives of a function at a point a are given by respectively, provided

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The right-sided and left-sided derivatives of a function at a point a are given by

f(a + h) – f(a) lim f(a + h) – f(a) lim f+'(a) and f-'(a) h→0+

respectively, provided these limits exist. The derivative f'(a) exists if and only if f₊'(a) = f_-'(a).

a. Sketch the following functions.

b. Compute f₊'(a) and f_-'(a) at the given point a.

c. Is f continuous at a? Is f differentiable at a?

f(x) [ 4 – x² if x < 1 2x + 1 ifx > l’

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Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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Question Posted: Feb 08, 2019 11:48 AM

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The right-sided and left-sided derivatives of a function at a point a are given by respectively, provided

Question:

f(a + h) – f(a) lim f(a + h) – f(a) lim f+'(a) and f-'(a) h→0+ f(x) [ 4 – x² if x < 1 2x + 1 ifx > l’ " ; a = 1

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a b Assuming the point a 1 we get because for h 0 we have 1 h ...View the full answer

Calculus Early Transcendentals

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