using differentiation prove that for every x in R on has

cosx>or= 1-(x^2)/2

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- Jan 18th 2010, 05:54 PMamm345How do you prove using differentiation?
using differentiation prove that for every x in R on has

cosx>or= 1-(x^2)/2 - Jan 18th 2010, 05:59 PMDrexel28
Let $\displaystyle f(x)=\cos(x)+\frac{x^2}{2}-1$. We have that $\displaystyle f(0)=0$ and $\displaystyle f'(x)=x-\sin(x)$. But if $\displaystyle g(x)=x-\sin(x)$ we see that $\displaystyle g(0)=0$ and $\displaystyle g'(x)=1-\cos(x)\geqslant 0$. Draw your conclusion.