# mathematics , calculus

verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.

f(x)=√x-1/3 x,[0,9]

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1. (f(9)-f(0))/9 = (0-0)/9 = 0
Since f(0) = f(9) we can apply Rolle's Theorem.

f'(x) = 1/(2√x) - 1/3
So, look for some value x=c such that f'(c) = 0
1/(2√c) = 1/3
2√c = 3
c = 9/4

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