(a) (i) Prove from the definition of differentiability that the function x+3 a-2 is differentiable at the point 1, and find f'(1). (ii) Sketch the graph of the function cos, x≤0, 1+x, x>0. Use a result or rule from the module to determine whether fis differentiable at 0.
(a) (i) Prove from the definition of differentiability that the function x+3 a-2 is differentiable at the point 1, and find f'(1). (ii) Sketch the graph of the function cos, x≤0, 1+x, x>0. Use a result or rule from the module to determine whether fis differentiable at 0.
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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Question
![(a) (i) Prove from the definition of differentiability that the function
x + 3
x-2
is differentiable at the point 1, and find f'(1).
(ii) Sketch the graph of the function
f(x)=
Use a result or rule from the module to determine whether fis
differentiable at 0.
cosa, a ≤0,
1+x, z>0.
(b) The function g is continuous on the interval [-2, 1] and differentiable on
the interval (-2, 1). Also,
g(-2) 1 and g(x)| ≤3 for a € (-2,1).
Use the Mean Value Theorem to prove that -8 ≤ g(1) ≤ 10.
(c) Prove the inequality
6x¹/6 ≤x+5
for a = [0, 1].
€
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Transcribed Image Text:(a) (i) Prove from the definition of differentiability that the function
x + 3
x-2
is differentiable at the point 1, and find f'(1).
(ii) Sketch the graph of the function
f(x)=
Use a result or rule from the module to determine whether fis
differentiable at 0.
cosa, a ≤0,
1+x, z>0.
(b) The function g is continuous on the interval [-2, 1] and differentiable on
the interval (-2, 1). Also,
g(-2) 1 and g(x)| ≤3 for a € (-2,1).
Use the Mean Value Theorem to prove that -8 ≤ g(1) ≤ 10.
(c) Prove the inequality
6x¹/6 ≤x+5
for a = [0, 1].
€
€
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