3. Let f(x) = ={ and x² if 0≤x≤ 1 √2x-x² if 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3. Let f(x) =
={
and
x²
if 0≤x≤ 1
√2x-x² if 1<x<2
A graph of y = f(x) is shown in the figure.
(a) Verify that f is continuous at x = 1.
(b) Use the Derivative Rules to evaluate the
one-sided derivatives of f at x = 1:
f'_(1) =
d (x²)),-1
dx
f(1) =
d
dx (v
=(√²x − x² ) | ₁₁
x=1
(c) Is f differentiable at x = 1?
MIN
y=f(x)
1
NIW
Transcribed Image Text:3. Let f(x) = ={ and x² if 0≤x≤ 1 √2x-x² if 1<x<2 A graph of y = f(x) is shown in the figure. (a) Verify that f is continuous at x = 1. (b) Use the Derivative Rules to evaluate the one-sided derivatives of f at x = 1: f'_(1) = d (x²)),-1 dx f(1) = d dx (v =(√²x − x² ) | ₁₁ x=1 (c) Is f differentiable at x = 1? MIN y=f(x) 1 NIW
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