Mean value theorem question?
determine whether f satisfies the hypotheses of the mean value on [a,b], and, if so, find all numbers c in (a,b) such that f(b) - f(a) = f'(c)(b-a).

f(x)= tan(x) [0,(pi/4)]

so i plugged the intervals in and got
f(0)=0 and f(pi/2)=1
f'(c)= sec^2(c)

Then i did (1-0)=sec^2(c)((pi/4)-0)

ended up getting sec^2(c)=(4/pi)

I'm not sure what to do from here... especially since a friend of mine got (4/pi) as an answer. Did i do something wrong? If not how do i finish this problem?

Question

Mean value theorem question?
determine whether f satisfies the hypotheses of the mean value on [a,b], and, if so, find all numbers c in (a,b) such that f(b) - f(a) = f'(c)(b-a).

f(x)= tan(x) [0,(pi/4)]

so i plugged the intervals in and got
f(0)=0 and f(pi/2)=1
f'(c)= sec^2(c)

Then i did (1-0)=sec^2(c)((pi/4)-0)

ended up getting sec^2(c)=(4/pi)

I'm not sure what to do from here... especially since a friend of mine got (4/pi) as an answer. Did i do something wrong? If not how do i finish this problem?

anonymous · Answer

i guess tangent is continuous on $[0\frac{\pi}{4}]$ so it does satisfy the hypothesis

anonymous · Answer

oh continuous and also differentiable

anonymous · Answer

also as you said
$$f(\frac{\pi}{4})-f(0)=1-0=1$$

anonymous · Answer

ans also as you said the derivative is $\sec^2(x)$ so your job is to solve 
$$\sec^2(x)=\frac{4}{\pi}$$ 
good luck with that!