f(x) = 6sqrt{x}- 9x n the interval [1,9].

Question

f(c)=f(9)-f(1)/9-(1)=?

Verify that the conclusion of the Mean Value Theorem holds by computing

Now find,c in (1, 9) so that f'(c) equals the answer you just found. c=?

Answer 1

f = 6√x - 9x
f' = 3/√x - 9

f(1) = -3
f(9) = 63
The avg slope is 33/4

So we want to find where the tangent has slope 33/4

3√x-9 = 33/4
3√x = 69/4
√x = 23/4
x = √23 / 2

So, is 1 < √23/2 < 9?

If so, the theorem applies.