5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1 < x -1, (a) Check if f(x) has a derivative at x = -1. If f(x) has a derivative at x = - then give the derivative. If not, explain why. (b) Check if f(x) has a derivative at x = 1. If yes, then give the derivative of f(x) at x = 1. If not, explain why.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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5. Consider the function f(x).
f(x)
=
2x² + 3x + 1
|x|
sin(x − 1) + 1
if x < -1
if - 1<x< 1
if 1 < x
= -1,
(a) Check if f(x) has a derivative at x = -1. If f(x) has a derivative at x =
then give the derivative. If not, explain why.
(b) Check if f(x) has a derivative at x = 1. If yes, then give the derivative of
f(x) at x = 1. If not, explain why.
Transcribed Image Text:5. Consider the function f(x). f(x) = 2x² + 3x + 1 |x| sin(x − 1) + 1 if x < -1 if - 1<x< 1 if 1 < x = -1, (a) Check if f(x) has a derivative at x = -1. If f(x) has a derivative at x = then give the derivative. If not, explain why. (b) Check if f(x) has a derivative at x = 1. If yes, then give the derivative of f(x) at x = 1. If not, explain why.
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