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

Question:

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’

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

Question Posted: