# Question #c6955

Jun 9, 2017

$\text{SP} : \left(\frac{1}{3} \sqrt{2} , \frac{4}{9} \sqrt{2}\right) , \left(- \frac{1}{3} \sqrt{2} , - \frac{4}{9} \sqrt{2}\right)$

#### Explanation:

$f \left(x\right) = 2 x - 3 {x}^{3}$

In order to find the stationary points if this function, we need to find $f '$ and solve it for $x$.

$f ' = 2 - 9 {x}^{2}$

Let $f ' = 0$

Then $2 - 9 {x}^{2} = 0$

$9 {x}^{2} = 2$

${x}^{2} = \frac{2}{9}$

$x = \pm \frac{\sqrt{2}}{3}$

We have found the $x$-coordinates of the stationary points and we know need to find the $y$-coordinates.

$f \left(\frac{\sqrt{2}}{3}\right) = \frac{4}{9} \sqrt{2}$

$f \left(- \frac{\sqrt{2}}{3}\right) = - \frac{4}{9} \sqrt{2}$

So the SP are $\left(1 \text{/"3sqrt2, 4"/"9sqrt2) and (-1"/"sqrt2, -4"/} 9 \sqrt{2}\right)$.