*y = f*'(

*x*)? First, let's take a look at the graph below:

Recall the concept

*f*'(

*a*) is the slope of

*f*(

*x*) at

*x = a*:

a) if

*f*(

*x*) is increasing,

*f*'(

*x*) > 0, which means the graph of

*y = f*'(

*x*) falls

**above**the

*x*-axis;

b) if

*f*(

*x*) is constant or reach to an extremum,

*f*'(

*x*) = 0, which means the graph of

*y = f*'(

*x*) falls

**on**the

*x*-axis;

c) if

*f*(

*x*) is decreasing,

*f*'(

*x*) < 0, which means the graph of

*y = f*'(

*x*) falls

**below**the

*x*-axis.

If you wish try out your understanding towards the concept above, perhaps you can ask your friend's help to give you a graph of a function (remember, a function is a one-to-one or many-to-one relationship) and you may try to sketch its derivative graph.

Betty, Created with GeoGebra

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