Posted by **saud** on Sunday, November 6, 2011 at 1:09am.

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 -
**MathMate**, Sunday, November 6, 2011 at 8:23am
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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