# Curve sketching: 2nd derivatives test

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!

 ArcSine Posts: 952, Reputation: 518 Senior Member #2 Oct 1, 2009, 08:14 AM
Just evaluate the original equation for x = 1/2.
 radiation Posts: 21, Reputation: 10 New Member #3 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 Posts: 2,272, Reputation: 1436 Ultra Member #4 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:

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

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