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Math Help - find the critical numbers of the function:

  1. #1
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    find the critical numbers of the function:

    f(x)=x^\frac{4}{5}(x-4)^2
    find the critical numbers of the function:

    f'(x)=\frac{4}{5}x^\frac{-1}{5}(x-4)^2 + 2(x-4)(x^\frac{4}{5})<br />

    factor a term out:
    x^\frac{-1}{5}(\frac{4}{5}(x-4)^2 + 2x^\frac{5}{5}(x-4))

    I see the 0 and 4, but the solution guide says there is also a critical number at \frac{8}{7}.
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  2. #2
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    (x-4) is a common factor so take it out the front too to get:
    x^(-1/5)(x-4)[(4/5)(x-4)+2x]

    Last bracket becomes (4/5)x-16/5+2x Set this =0 and solve to get the third solution.
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