Question

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval.
f(x) = square root of x
interval: [0, 25]

I've gotten all the way to solving for f'(x), but for some reason my answer isn't working. Anyone have any ideas?

Answer 1

What do you understand the Mean Value Theorem to be?

Answer 2

f'(c) = f(b) - f(a)/ b-a
i solved that and found of f'(c) to be 1/5
so i solved for f'(x) which is 1/2x^-1/2 and plugged in the 1/5.
does that answer your question?

Answer 3

Yes, ok, what you want to do is set 1/2x^-1/2 = 1/5.
You want to find the x where the slope of the tangent line is equal to the slope of the secant line.

Answer 4

that's where i got stuck. it didn't accept my answer as - square root of 2/5 or in decimal form, so i wasn't sure what to do

Answer 5

don't square root 2/5, square 5/2

Answer 6

okay thank you, i'll try that(:

Answer 7

\[\large 0.5x^{-1/2}=0.2\]
\[\large x^{-1/2}=0.4\]
\[\large x^{-1}=0.16\]
\[\large x=25/4\]

Answer 8

that worked thank you very much

Answer 9

You're welcome.
You had the general idea, just had to be more careful with the algebra.