#f# is some differentiable function. #f'#, the derivative of #f# is shown below [note, is not the graph of f itself]. Use the graph to answer the following questions [For parts (a)-(c), select all that apply]? (See image below)

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1 Answer
Mar 11, 2017

See below.

Explanation:

#f# is increasing where #f'# is positive. That is, where the graph of #f'# is above the #x# axis.

#f# is decreasing where #f'# is negative. That is, where the graph of #f'# is below the #x# axis.

The critical values are the #x# intercepts.

Without knowing the function, we cannot find the minima and maxima (or minimums and maximums, if you insist).

But we CAN find the #x# values where minima occur.

#f# has a minimum where #f'# changes from negative to positive. (In this example at #x=-4# and at #x=1#.)

#f# has a maximum where #f'# changes from positive to negative. (In this example at #x=3#.)