Explanation Given information: The function f ( x ) = { x 3 x ≤ 0 x x > 0 Concept used: A function f ( x ) is differentiable at any point x = a , when the left hand derivative and right hand derivative are equal and give a finite quantity. Here, left hand derivative f ′ ( a − ) = lim x → a f ( a − x ) − f ( a ) ( − x ) and Right hand derivative f ′ ( a + ) = lim x → a f ( a + x ) − f ( a ) ( x ) Consider the function, f ( x ) = { x 3 x ≤ 0 x x > 0 Now, left hand derivative of the function at x = 0 is, f ′ ( 0 − ) = lim x → 0 <

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

21st Edition

ISBN: 9781319438333

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 3.1, Problem 48E

To determine

To prove:

That f is not differentiable at x=0 and has a corner in its graph.

Here, f(x)={x3 x≤0x x>0

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Chapter 3.1, Problem 47E

Chapter 3.1, Problem 49E

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Chapter 3 Solutions

ACHIEVE FOR CALCULUS 4 TERM >CSI CUSTOM<

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To prove: That f is not differentiable at x = 0 and has a corner in its graph. Here, f ( x ) = { x 3 x ≤ 0 x x > 0

Solution Summary: The author explains that the function f(x) is not differentiable at x=0 and has a corner in its graph.

Concept explainers

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To prove:

That f is not differentiable at x=0 and has a corner in its graph.

Here, f(x)={x3 x≤0x x>0

Want to see the full answer?

Chapter 3 Solutions

To prove: That f is not differentiable at x = 0 and has a corner in its graph. Here, f ( x ) = { x 3 x ≤ 0 x x &gt; 0

Solution Summary: The author explains that the function f(x) is not differentiable at x=0 and has a corner in its graph.

Concept explainers

Videos

To prove: That f is not differentiable at x=0 and has a corner in its graph. Here, f(x)={x3 x≤0x x>0

Want to see the full answer?

Chapter 3 Solutions

To prove: That f is not differentiable at x = 0 and has a corner in its graph. Here, f ( x ) = { x 3 x ≤ 0 x x > 0

To prove:

That f is not differentiable at x=0 and has a corner in its graph.

Here, f(x)={x3 x≤0x x>0