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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- Dec 7th 2009, 05:45 PMreynardinCubic 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? - Dec 7th 2009, 06:19 PMHaversine
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. - Dec 7th 2009, 06:22 PMreynardin
thanks, I got it (Clapping)