All High School Math Resources
Example Questions
Example Question #1 : Derivatives
The function is such that
When you take the second derivative of the function , you obtain
What can you conclude about the function at ?
The point is an absolute minimum.
The point is a local maximum.
The point is an absolute maximum.
The point is a local minimum.
The point is an inflection point.
The point is an inflection point.
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 #4 : Pre Calculus
Consider the function
Find the maximum of the function on the interval .
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.
All High School Math Resources
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