Curve sketching: 2nd derivatives test

ArcSine · Oct 1, 2009, 08:14 AM

Just evaluate the original equation for x = 1/2.

radiation · Oct 4, 2009, 03:17 AM

I think thr is some error in your ans.. For x=1/2, the only value for why is -13/12..

galactus · Oct 4, 2009, 04:08 AM

Quote:

Gud day!

I just want to know what is the correct answer in this problem:

Equation:
$y = 1/3 x^{3} - 1/2 x^{2} - 2x$
The point of inflection that I got is (1/2 , -3/4) but according to the book its (1/2, -13/12). How do they get that?

Thanks!

They found the second derivative, set to 0 and solved for x.

$y'=x^{2}-x-2$

$y''=2x-1$

$2x-1=0\Rightarrow x=\frac{1}{2}$

Plug back into original equation:

$\frac{1}{3}(\frac{1}{2})^{3}-\frac{1}{2}(\frac{1}{2})^{2}-2(\frac{1}{2})=\frac{-13}{12}$

Curve sketching: 2nd derivatives test

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