Question #2bc16

Jan 31, 2018

The points are: $\left(- 5 , 8\right) , \left(6 , 327\right)$

Explanation:

You do part b. the same way that you did part a. except that you set the first derivative equal to 144, instead of 0.

$f ' \left(x\right) = 6 {x}^{2} - 6 x - 36 = 144$

$6 {x}^{2} - 6 x - 180 = 0$

${x}^{2} - x - 30 = 0$

$\left(x + 5\right) \left(x - 6\right) = 0$

$x = - 5$ and $x = 6$

The corresponding y coordinates are:

$f \left(- 5\right) = 2 {\left(- 5\right)}^{3} + 3 {\left(- 5\right)}^{2} - 36 \left(- 5\right) + 3$ and $f \left(6\right) = 2 {\left(6\right)}^{3} + 3 {\left(6\right)}^{2} - 36 \left(6\right) + 3$

$f \left(- 5\right) = 8$ and $f \left(6\right) = 327$

The points are: $\left(- 5 , 8\right) , \left(6 , 327\right)$