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Example Questions
Example Question #9 : Graph Functions And Their First And Second Derivatives
The following is the graph of the derivative of :
From the graph of the derivative, which of the following is correct?
There are points of inflection at and
is concave up on the interval
and concave down on the interval
is decreasing from
and decreasing on the intervals
and
is concave down on the interval
and concave up on the interval
is concave up on the interval
and concave down on the interval
We know that our function will be concave up when the derivative is increasing and concave down when the derivative is decreasing. The graph of the derivative is increasing on the interval and so
will be concave up on this interval. The graph of the derivative is decreasing on the interval
and so
will be concave down on this interval.
Example Question #10 : Graph Functions And Their First And Second Derivatives
True or False: An increasing derivative means that the function must be positive
True
False
False
Just because a derivative is increasing does not mean that the function will be positive. We know that if the derivative is increasing, then the function must be concave up. We are given no insight as to where the function starts and no insight as to whether the function is positive or negative.
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