Cubic Polynomial Functions

I'm not quite sure where to start with this problem:

Let f(x) = ax^3 +bx^2 + cx + d, a != 0
a) show that f has either 0 or 2 local extrema.
b) give an example of each possibility in part (a)

Can somebody start me off on the right track?

Quote:

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Originally Posted by reynardin

I'm not quite sure where to start with this problem:

Let f(x) = ax^3 +bx^2 + cx + d, a != 0
a) show that f has either 0 or 2 local extrema.
b) give an example of each possibility in part (a)

Can somebody start me off on the right track?

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The derivative will help you.

Let's say your original equation is a cubic. The derivative will be some quadratic. A quadratic always has two roots. If one is real, then they both are real, and there must be two real 'zeros' for the derivative. If one is imaginary, then both are imaginary.

thanks, I got it (Clapping)