## anonymous 3 years ago Determine whether the Mean Value Theorem for Derivatives applies for F(x)= x-cosx, on [x/2,-x/2] and find the coordinates of the points whose existence is guaranteed by the theorem

1. anonymous

hmm what a weird looking interval you have

2. anonymous

Scratch that make it [pi/2,-pi/2]

3. anonymous

no such interval

4. anonymous

[-pi/2,pi/2]

5. anonymous

that makes sense yes, the mvt applies because your function is continuous how you are going to solve i have no idea, but $f(x)=x-\cos(x)$ so $$f(\frac{\pi}{2})=\frac{\pi}{2}-\cos(\frac{\pi}{2})=\frac{\pi}{2}-0=\frac{\pi}{2}$$

6. anonymous

and $f(-\frac{\pi}{2})=-\frac{\pi}{2}$ similar to above therefore $\frac{f(\frac{\pi}{2})-f(-\frac{\pi}{2})}{\frac{\pi}{2}+\frac{\pi}{2}}$ $=\frac{(\frac{\pi}{2}+\frac{\pi}{2})}{\pi}=1$

7. anonymous

and $f'(x)=1+\sin(x)$ so you need so solve $1+\sin(x)=1$ for $$x$$ in the interval should not be too hard actually

8. anonymous

Right so I take the arcsin of 0 and get the answer?