Graph of f '(x)

Ever think of drawing the graph of y = f '(x)? First, let's take a look at the graph below. The blue solid curve is the graph of f (x), and the green dotted curve is f '(x).



Recall the concept f '(a) is the slope of f(x) at x = a, while comparing with the graph above:
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 any 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