Finding Values for Mean Value Theorem in Integrals

[vee123]

I'm having a some difficulty with this problem:

Fidn the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the indicated interval:

f(x)=x - 2(square root of x) Interval: [0,2]

I found the integral to be: x^2/2 - 4/3 x^3/2, then I solved for the interval and got 2- 8(square root of 2)/3
then I did this:
f(c)(2-0)= 2- 8(square root of 2)/3

I just want to know if I am doing this correctly because I can't seem to get the right answers (0.4380,1.7908)

 

[MathStudent]

your methods are correct so far.

you should have an equation that involves $c$ and $\sqrt{c}$

hint: to solve this equation form the quadratic equation in u, by substituting $u = \sqrt{c}$

-MS

 

[vee123]

Thanks! I think I know what to do now. I really appreciate it!