High School Math : Finding Maxima and Minima

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Finding Maxima And Minima

The function  is such that

 

When you take the second derivative of the function , you obtain 

What can you conclude about the function at ?

Possible Answers:

The point is an inflection point.

The point is a local maximum.

The point is an absolute minimum.

The point is an absolute maximum.

The point is a local minimum.

Correct answer:

The point is an inflection point.

Explanation:

We have a point at which . We know from the second derivative test that if the second derivative is negative, the function has a maximum at that point. If the second derivative is positive, the function has a minimum at that point. If the second derivative is zero, the function has an inflection point at that point.

Plug in 0 into the second derivative to obtain 

So the point is an inflection point.

Example Question #2 : Introductory Calculus

Consider the function 

Find the maximum of the function on the interval .

Possible Answers:

Correct answer:

Explanation:

Notice that on the interval , the term  is always less than or equal to . So the function is largest at the points when . This occurs at  and .

Plugging in either 1 or 0 into the original function  yields the correct answer of 0.

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