calculus

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Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval.
f(x)=x^−1 [1,9]

  • calculus -

    f(1)=1/1=1
    f(9)=1/9
    The mean slope is ((1/9)-1)/(9-1)= -1/9

    Now calculate f'(x)=-1/x²
    So we need to solve for
    f'(x)=-1/9
    which gives x=3 or -3.
    Since only x=3 is on the interval [1,9], this is the only solution, i.e. c=3.

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