Precalculus : Rate of Change Problems

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #11 : Derivatives

If the average rate of change of  between  and , where , is positive, then what can be said about  on that interval?

Possible Answers:

 is decreasing

 is odd

 is increasing

 is constant

Correct answer:

 is increasing

Explanation:

If the average rate of change is positive, then the formula gives us , so . We know  because it is a given in the proble, so . Hence 

 and . This shows that  must increase over the interval from  to .

Example Question #12 : Rate Of Change Problems

If the average rate of change of  between  and , where , is negative, then what can be said about  on that interval?

Possible Answers:

 is decreasing

 is negative

 is an odd function

 is constant

 is increasing

Correct answer:

 is decreasing

Explanation:

If the average rate of change is negative, then the function is changing in a negative direction overall. Hence, the graph of the function will be decreasing on that interval.

 and since  is decreasing

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