# Question #f36b9

Jan 25, 2018

Refer explanation.

#### Explanation:

Given -

$y = {x}^{4} + 8 {x}^{3}$

To graph, a function, first find the turning points.
Find the first derivative and set it to zero, so that you know the value of $x$, the slope of the curve becomes zero.

$\frac{\mathrm{dy}}{\mathrm{dx}} = 4 {x}^{3} + 24 {x}^{2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 0 \implies 4 {x}^{3} + 24 {x}^{2} = 0$

$4 {x}^{2} \left(x + 6\right) = 0$

$4 {x}^{2} = 0$

$x = 0$

$x = - 6$

At $x = 0$ and at $x = - 6$, there are turning points.
Take a range of values that includes 0 and -6. Calculate the corresponding value of $y$. Tabulate them. Use the pair of the points to obtain the curve.

At $x = 0$, there is a point of inflexion.
At $x = - 8$, the curve reaches the minimum.