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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

On the graph below, locate any points of inflection (approximately) and label where the curve satisfies f " ( x )   >   0   and  f " ( x )   < 0 .

Chapter 10.2, Problem 3CP, 3. On the graph below, locate any points of inflection (approximately) and label where the curve

To determine

The points of inflection and the region on the curve where f(x)>0 and f(x)<0 for the provided graph of the function,

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 10.2, Problem 3CP

Explanation

Given Information:

The provided graph of a function is,

Explanation:

Consider the provided graph,

Now, recall that the points of inflection are the values of x for which the value of the second derivative of the function is 0, that is f(x)=0.

Thus, f(x)=0 in the graph wherever the graph changes its concavity.

Mark the three points where the graph changes its concavity as A, B and C.

Since, at the points A, B and C the function satisfies f(x)=0.

Thus, the points of inflection are A, B and C.

Since, f(x) is the first derivative of f(x), wherever the graph of f(x) is increasing, it follows that f(x)>0

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Chapter 10 Solutions

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