High School Math : Finding Maxima and Minima

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #6 :Pre Calculus

The functionis 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 absolute minimum.

The point is an inflection point.

The point is an absolute maximum.

The point is a local minimum.

The point is a local maximum.

有限公司rrect 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 #7 :Pre Calculus

有限公司nsider the function

Find the maximum of the function on the interval.

Possible Answers:

有限公司rrect answer:

Explanation:

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

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

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