Show that the function f(x) = |x - 3| is not differentiable at 3. We have x- 3 if x 2 3 f(x) = |x - 3| = -(x- 3) if x< 3. The right-hand limit is lim X-3+ f(x) – f(3) 1 X - 3 and the left-hand limit is f(x) - f(3) lim -1 X-3 x - 3 f(x) - f(3) Since these limits are not equal, f'(3) = lim X3 does not exist and f is not differentiable at 3. x - 3 Find a formula for f'and sketch its graph. if x > 3 f'(x) =- if x < 3 Graph Layers 6 After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill No Solutio
Show that the function f(x) = |x - 3| is not differentiable at 3. We have x- 3 if x 2 3 f(x) = |x - 3| = -(x- 3) if x< 3. The right-hand limit is lim X-3+ f(x) – f(3) 1 X - 3 and the left-hand limit is f(x) - f(3) lim -1 X-3 x - 3 f(x) - f(3) Since these limits are not equal, f'(3) = lim X3 does not exist and f is not differentiable at 3. x - 3 Find a formula for f'and sketch its graph. if x > 3 f'(x) =- if x < 3 Graph Layers 6 After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill No Solutio
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.5: Polynomial And Rational Functions
Problem 41E
Related questions
Question
just need the last 2 please
![Show that the function f(x) = |x – 3| is not differentiable at 3.
We have
х— 3
if x > 3
f(x) = |x - 3| =
-(x- 3)
if x < 3.
The right-hand limit is
f(x) – f(3)
lim
1
х — 3
X→3+
and the left-hand limit is
f(x) – f(3)
lim
-1
х— 3
X→3-
Since these limits are not equal, f'(3) :
f(x) – f(3)
lim
does not exist and f is not differentiable at 3.
X→3
х — 3
Find a formula for f'and sketch its graph.
if x > 3
f'(x) =
if x < 3
Graph Layers
«
Clear All
6
After you add an object to the graph you
Delete
can use Graph Layers to view and edit its
4
properties.
3
Fill
2
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
6
-1
No
-2
Solution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f05c2dc-fe57-4c83-8b9c-00e421533115%2F3cc49c13-1bc7-470e-84a7-5533d0fa6184%2F542i6zr_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the function f(x) = |x – 3| is not differentiable at 3.
We have
х— 3
if x > 3
f(x) = |x - 3| =
-(x- 3)
if x < 3.
The right-hand limit is
f(x) – f(3)
lim
1
х — 3
X→3+
and the left-hand limit is
f(x) – f(3)
lim
-1
х— 3
X→3-
Since these limits are not equal, f'(3) :
f(x) – f(3)
lim
does not exist and f is not differentiable at 3.
X→3
х — 3
Find a formula for f'and sketch its graph.
if x > 3
f'(x) =
if x < 3
Graph Layers
«
Clear All
6
After you add an object to the graph you
Delete
can use Graph Layers to view and edit its
4
properties.
3
Fill
2
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
6
-1
No
-2
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