Show that the function f(x) = |x2| is not differentiable at 2. We have if x ≥ 2 f(x) = |x-21= if x < 2. The right-hand limit is lim f(x) - f(2) *-2* x-2 and the left-hand limit is lim F(x) - F(2) x-2 x-2 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 Find a formula for f' and sketch its graph. x-2 f'(x) = No Solution Help if x 2 if x < 2 7 Clear All Graph Layers B 5 4 3 2 + B -6 -4 -3 2 -1 2 5 1 2 3 4 5 Delete After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.8: Linear And Quadratic Functions
Problem 2WE
Question
Show that the function f(x) = |x2| is not differentiable at 2.
We have
if x ≥ 2
f(x) = |x-21=
if x < 2.
The right-hand limit is
lim
f(x) - f(2)
*-2* x-2
and the left-hand limit is
lim F(x) - F(2)
x-2
x-2
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
Find a formula for f' and sketch its graph.
x-2
f'(x) =
No
Solution
Help
if x 2
if x < 2
7
Clear All
Graph Layers
B
5
4
3
2
+
B
-6
-4
-3
2
-1
2
5
1
2
3
4
5
Delete
After you add an object to the graph you
can use Graph Layers to view and edit its
properties.
Fill
Transcribed Image Text:Show that the function f(x) = |x2| is not differentiable at 2. We have if x ≥ 2 f(x) = |x-21= if x < 2. The right-hand limit is lim f(x) - f(2) *-2* x-2 and the left-hand limit is lim F(x) - F(2) x-2 x-2 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 Find a formula for f' and sketch its graph. x-2 f'(x) = No Solution Help if x 2 if x < 2 7 Clear All Graph Layers B 5 4 3 2 + B -6 -4 -3 2 -1 2 5 1 2 3 4 5 Delete After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill
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