# Math Help - Help in mean value theory

1. ## Help in mean value theory

I don't know how to use mean value theorem to show that
e^x >= 1+x+ 1/2 x^2 for x>0
I hope someone can give me some advises.
Really thanks.

2. You don't really need the mean value theorem here (though you do need basic knowledge of Taylor Series), because it can be shown that

$\displaystyle e^x = \sum_{n = 0}^{\infty}\frac{1}{n!}x^n$

$\displaystyle = 1 + x + \frac{1}{2}x^2 + \frac{1}{3!}x^3 + \frac{1}{4!}x^4 + \dots$

$\displaystyle \geq 1 + x + \frac{1}{2}x^2$.

3. I know it can use Taylor theorem .
But I want to use another way to do it.
So I am thinking whether mean value theorem can do it or not.
And want to try it