# How do you find the stationary points of a function?

Jun 26, 2018

Shown below

#### Explanation:

As we can see from this image, a stationary point is a point on a curve where the slop is zero

Hence the stationary points are when the derivative is zero

Hence to find the stationary point of $y = f \left(x\right)$, find $\frac{\mathrm{dy}}{\mathrm{dx}}$ and then set it equal to zero

$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

Then solve this equation, to find the values of $x$ for what the function is stationary

For examples

$y = {x}^{2} + 3 x + 8$

To find the stationary find $\frac{\mathrm{dy}}{\mathrm{dx}}$

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

Set it to zero

$2 x + 3 = 0$

Solve

$x = - \frac{3}{2} \implies y = \frac{23}{4}$

Hence the stationary point of this function is at $\left(- \frac{3}{2} , \frac{23}{4}\right)$