How do you prove using differentiation?

• January 18th 2010, 05:54 PM
amm345
How do you prove using differentiation?
using differentiation prove that for every x in R on has
cosx>or= 1-(x^2)/2
• January 18th 2010, 05:59 PM
Drexel28
Quote:

Originally Posted by amm345
using differentiation prove that for every x in R on has
cosx>or= 1-(x^2)/2

Let $f(x)=\cos(x)+\frac{x^2}{2}-1$. We have that $f(0)=0$ and $f'(x)=x-\sin(x)$. But if $g(x)=x-\sin(x)$ we see that $g(0)=0$ and $g'(x)=1-\cos(x)\geqslant 0$. Draw your conclusion.