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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d94971-c4ee-4188-b521-ed6cff9deaa9%2Fbed639be-5cba-4ca1-bc8c-c6788e1ac75b%2Fla3gv7c_processed.png&w=3840&q=75)
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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