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Show that the function f(x) = |x-2] is not differentiable at 2. We have The right-hand limit is f(x) = f(2) lim x→2+ X-2 and the left-hand limit is lim X-2- f'(x) = f(x) = |x - 2| = f(x) = f(2) X-2 O Find a formula for f' and sketch its graph. No Solution Since these limits are not equal, f'(2) = lim F(X) - 1(2) does not exist and f is not differentiable at 2. x → 2 X-2 ? Help = = -7 -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 if x ≥ 2 1 if x < 2. 2 3 4 5 6 Clear All Fill Graph Layers << After you add an object to the graph you can use Graph Layers to view and edit its properties.

Show that the function f(x) = |x-2] is not differentiable at 2. We have The right-hand limit is f(x) = f(2) lim x→2+ X-2 and the left-hand limit is lim X-2- f'(x) = f(x) = |x - 2| = f(x) = f(2) X-2 O Find a formula for f' and sketch its graph. No Solution Since these limits are not equal, f'(2) = lim F(X) - 1(2) does not exist and f is not differentiable at 2. x → 2 X-2 ? Help = = -7 -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 if x ≥ 2 1 if x < 2. 2 3 4 5 6 Clear All Fill Graph Layers << After you add an object to the graph you can use Graph Layers to view and edit its properties.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q11. Please answer all the parts to this question 

Show that the function f(x) = |x - 2] is not differentiable at 2. We have The right-hand limit is f(x) = f(2) lim x→2+ X-2 and the left-hand limit is lim X-2- f'(x) = f(x) = |x - 2| = f(x) = f(2) X-2 O Find a formula for f' and sketch its graph. No Solution = Since these limits are not equal, f'(2) = lim F(x) = f(2) does not exist and f is not differentiable at 2. x → 2 X-2 ? Help = -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 if x ≥ 2 1 if x < 2. 2 3 4 5 6 Clear All 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) = |x - 2] is not differentiable at 2. We have The right-hand limit is f(x) = f(2) lim x→2+ X-2 and the left-hand limit is lim X-2- f'(x) = f(x) = |x - 2| = f(x) = f(2) X-2 O Find a formula for f' and sketch its graph. No Solution = Since these limits are not equal, f'(2) = lim F(x) = f(2) does not exist and f is not differentiable at 2. x → 2 X-2 ? Help = -6 -5 -4 if x > 2 if x < 2 -3 -2 -1 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 if x ≥ 2 1 if x < 2. 2 3 4 5 6 Clear All 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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