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Q. 83

Found in: Page 276


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

In Exercises 83–86, use the given derivative f' to find any local extrema and inflection points of f and sketch a possible graph without first finding a formula for f.


The possible graph of f is

See the step by step solution

Step by Step Solution

Step 1. Given Information.

The given derivative function is f'(x)=x3-3x2+3x.

Step 2. Apply the first derivative test.

To find the local extrema the first derivative of the function must be zero.



Thus, by the first derivative test, f has a local minimum at x=0.The function has no local maxima.

Step 3. Finding inflection points.

An inflection point occurs when f''(x)=0.

To find the inflection points, use the second derivative test.



Thus, the function has an inflection point at x=1. It is positive everywhere. Hence the graph of f will be concave up everywhere.

Step 4. Sketch the graph of function f.   

The graph of the function is

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