Question

Let the function be continuous on (a,b) and be differentiable on (a,b) except possibly at its critical point c. Then moving across c from left to right,f'
does not change sign at cu
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Answer 1

Answer:

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Step-by-step explanation:

what is the question

Answer 2

Moving across c from left to right, f' changes sign.

Given:

The function is continuous and differentiable on (a,b) and c is the critical point.

To find:
If f' changes sign at c.

Solution:

A critical point is where either the function is not differentiable or f'=0.

As the function is differentiable and continuous, f'=0 at c.
Hence it changes the sign at c.

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