Calculus AB : Analytical Applications of Derivatives

Study concepts, example questions & explanations for Calculus AB

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Example Questions

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Example Question #9 : Graph Functions And Their First And Second Derivatives

The following is the graph of the derivative of :

Q9

 

From the graph of the derivative, which of the following is correct?

Possible Answers:

 is decreasing from  and decreasing on the intervals  and 

There are points of inflection at  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 

Correct answer:

 is concave up on the interval  and concave down on the interval 

Explanation:

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 #1 : Graph Functions And Their First And Second Derivatives

True or False: An increasing derivative means that the function  must be positive

Possible Answers:

False

True

Correct answer:

False

Explanation:

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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