Verifying mean value question

[chibiemu]

Hello! Can someone help me with this question?

Verify the mean value theorem for f(x)=sinx on [0, π /2]

So far, I got f(0)=0 and f(π /2)=1 and then I plugged those numbers into [f(b)-f(a)]/[b-a] and got 2/π.

I am not sure where to go next.

 

[Dr.Peterson]

Hello! Can someone help me with this question?

Verify the mean value theorem for f(x)=sinx on [0, π /2]

So far, I got f(0)=0 and f(π /2)=1 and then I plugged those numbers into [f(b)-f(a)]/[b-a] and got 2/π.

I am not sure where to go next.

Well, what does the MVT say? Something about the derivative?

Find f'(x), and solve to find where it is equal to 2/π.

 

[Steven G]

MVT says that if
1) f(x) is continuous on [a,b],
2) f(x) is differentiable on (a,b), then
3) there exists a c in (a,b) such that f'(c) = [f(b)-f(a)]/(b-a)

You need to verify ALL 3 conditions list above, including the 1st two.