a. Let f(x) = { 2 sin(2 – x) – 4, x< 2, - 2x, x > 2. Is f differentiable at r = 2? b. Let (2h(x) + x)² f(x) = x +2 where h : R -→ R is a differentiable function. Show that f is differentiable at r = 2. Find f'(2) given that h(2) = 1 and h'(2) = 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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a. Let
{
2 sin(2 — a) — 4, г <2,
-2x,
f(x) =
x > 2.
Is f differentiable at x = 2?
b. Let
(2h(x) + x)²
f(x) =
%3|
x + 2
where h : R R is a differentiable function. Show that f is
differentiable at x = 2. Find f'(2) given that h(2) = 1 and h'(2)
1.
Transcribed Image Text:a. Let { 2 sin(2 — a) — 4, г <2, -2x, f(x) = x > 2. Is f differentiable at x = 2? b. Let (2h(x) + x)² f(x) = %3| x + 2 where h : R R is a differentiable function. Show that f is differentiable at x = 2. Find f'(2) given that h(2) = 1 and h'(2) 1.
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