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Math Help - Cubic Polynomial Functions

  1. #1
    Junior Member reynardin's Avatar
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    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?
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  2. #2
    Junior Member
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    Quote Originally Posted by reynardin View Post
    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?
    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.
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  3. #3
    Junior Member reynardin's Avatar
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    thanks, I got it
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