Graph the Equation $y = x \sqrt { 7 - x ^ { 2 } }$

Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points.
- $y = x \sqrt { 7 - x ^ { 2 } }$

A) local minimum: $\left( - \frac { \sqrt { 14 } } { 2 } , - \frac { 7 } { 2 } \right)$
local maximum: $\left( \frac { \sqrt { 14 } } { 2 } , \frac { 7 } { 2 } \right)$
inflection point: $( 0,0 )$


B) local maximum: $\left( \frac { 14 } { 3 } , \frac { 2 \cdot 7 ^ { 3 / 2 } \cdot \sqrt { 3 } } { 9 } \right)$
$\text { no inflection point. }$



C) local maximum: $( 0 , \sqrt { 7 } )$
no inflection points.


D) local minimum: $\left(-\frac{\sqrt{21}}{3},-\frac{2 \cdot 7^{3 / 2} \cdot \sqrt{3}}{9}\right)$
local maximum: $\left(\frac{\sqrt{21}}{3}, \frac{2 \cdot 73 / 2 \cdot \sqrt{3}}{9}\right)$
inflection point: $(0,0)$