### Home > APCALC > Chapter 10 > Lesson 10.1.1 > Problem10-11

10-11.

Multiple Choice: No calculator! A point of inflection for the curve $y = \frac { 12 } { x ^ { 2 } + 4 }$ is:

1. $( - \frac { 2 \sqrt { 3 } } { 3 } , \frac { 9 } { 4 } )$

1. $( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { 9 } { 4 } )$

1. $(0, 3)$

1. $( \sqrt { 2 } , 2 )$

1. $( - \sqrt { 2 } , 2 )$

$y^\prime=-12(x^2+4)^{-2}(2x)=-24x(x^2+4)^{-2}$

$y^{\prime\prime}=-24(x^2+4)^{-2}+48x(x^2+4)^{-3}(2x)$

Set $y^{\prime\prime} = 0$ and solve for $x$.

It may seem like there are two possible answers. Graph the function to check your results.