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Math

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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x)=x^(4/5)(x − 6)^2

  • Math - ,

    by the product rule ....

    f ' (x) = x^(4/5) (2)(x-6) + (4/5)x^(-1/5) (x-6)^2
    = (-1/5)x^(-1/5) (x-6) [10x + 4(x-6) ]
    = (-2/5)x^(-1/5) (x-6) (7x-12)

    = 0 for critical numbers (max,min)

    -1/5x^(-1/5) = 0 ---> no solution
    x-6 = 0 ---> x = 6
    7x-12=0 ---> x = 12/7

    take it from there

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