Given the function #f(x)=-(-5x+25)^(1/2_#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [3,5] and find the c?

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Answer 1 · 2017-04-23T17:35:09

See below.

The hypotheses af MVT are

f is continuous on #[3,5]#
f is differentiable on #(3,5)#

If the both statements are true, then #f# satisfies the hypotheses of the Mean Value Theorem on the interval.

To find the #c# mentioned in the conclusion of the theorem you need to find #f'(x)# and find #(f(5)-f(3))/(5-3)# and solve the equation:

#f'(x) = (f(5)-f(3))/(5-3)#.

Discard any solutions outside #(3,5)#.