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Determine if Rolle's Theorem can be applied. If it can, find all values of c such that f'(c)=0.

f(x)=x^3-9x, [-3,3]

  • Calculus -

    f(x) is continuous over the domain. [-3,3]

    f(x) is differential.
    f'(x) = 3x2 -9

    f(x) has two equal value points on the independent axis.
    f(-3) = f(3) = 0

    Therefore Rolle's Theorem Applies
    .: Exists c such that f'(c)=0

    Solve for c:
    0 = 3c2 - 9


  • Calculus -

    Ahh! That's the answer I had but I was doubting it because my partner got something else! Thanks!

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