# Math Help - Prove using the mean value theorem

1. ## Prove using the mean value theorem

Using mean value theorem , prove that
$tan x > x$ for all $x \boldsymbol{\epsilon} ( 0, \frac{\pi}{2} )$

2. For all x in (0,pi/2) there is a c in (0,x) such that

[tan(x)-tan(0)]/[x-0] = sec^2(c) > 1 for c in (0,pi/2)

tan(x)/x > 1

tan(x) > x

3. ## I did get this part

Originally Posted by Calculus26
For all x in (0,pi/2) there is a c in (0,x) such that

[tan(x)-tan(0)]/[x-0] = sec^2(c) > 1 for c in (0,pi/2)

tan(x)/x > 1

tan(x) > x

I didnt get this part could u please explain

[tan(x)-tan(0)]/[x-0] = sec^2(c)

4. Originally Posted by zorro
I didnt get this part could u please explain

[tan(x)-tan(0)]/[x-0] = sec^2(c)
that is just applying the mean value theorem. [f(b)-f(a)] / (b-a) = f'(c), in this case a=0, b=x, and f(x) = tan(x) so f'(x) = sec^2(x).