Derivatives of Cubic Functions


Problem

f(x) is a cubic function.
Then f'(x) is quadratic function.
There are three cases about the discriminant of f'(x).
Let f'(x) = ax2+bx+c, discriminant = b2-4ac.

(Figure 1) The discriminant is positive( not zero).

(Figure 2) The discriminant is positive( = zero).

(Figure 3) The discriminant is negative.

Figure 1
 Figure 2
 Figure 3

Applet