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Show that the function f(x) = |x - 21 is not differentiable at 2. We have The right-hand limit is f(x) = f(2) X-2 f(x) = |x2| = lim x→2+ and the left-hand limit is lim X-2- f(x) = f(2) X-2 f'(x) = = = Since these limits are not equal, f'(2) = lim x→2 Find a formula for f' and sketch its graph. if x > 2 if x < 2 if x ≥ 2 if x < 2. f(x) = f(2) x - 2 does not exist and f is not differentiable at 2.

Show that the function f(x) = |x - 21 is not differentiable at 2. We have The right-hand limit is f(x) = f(2) X-2 f(x) = |x2| = lim x→2+ and the left-hand limit is lim X-2- f(x) = f(2) X-2 f'(x) = = = Since these limits are not equal, f'(2) = lim x→2 Find a formula for f' and sketch its graph. if x > 2 if x < 2 if x ≥ 2 if x < 2. f(x) = f(2) x - 2 does not exist and f is not differentiable at 2.

Calculus: Early Transcendentals
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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Show that the function f(x) = |x2| is not differentiable at 2. We have The right-hand limit is f(x) = f(2) X-2 lim X→2+ and the left-hand limit is lim X-2- f(x) = |x2| = f(x) = f(2) X-2 f'(x) = = Since these limits are not equal, f'(2) = lim X→2 O = Find a formula for f' and sketch its graph. -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 A 7 6 5 4 3 2 1 if x ≥ 2 if x < 2. - f(x) = f(2) X-2 2 3 does not exist and f is not differentiable at 2. 177 Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.
Transcribed Image Text:Show that the function f(x) = |x2| is not differentiable at 2. We have The right-hand limit is f(x) = f(2) X-2 lim X→2+ and the left-hand limit is lim X-2- f(x) = |x2| = f(x) = f(2) X-2 f'(x) = = Since these limits are not equal, f'(2) = lim X→2 O = Find a formula for f' and sketch its graph. -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 A 7 6 5 4 3 2 1 if x ≥ 2 if x < 2. - f(x) = f(2) X-2 2 3 does not exist and f is not differentiable at 2. 177 Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties.
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