How do you find the stationary points of the function y=x^2+6x+1?

Apr 10, 2018

$\left(- 3 , - 8\right)$

Explanation:

The stationary points of a function are when $\frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$y = {x}^{2} + 6 x + 1$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x + 6$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 0 = 2 x + 6$

$x = - \frac{6}{2} = - 3$

${\left(- 3\right)}^{2} + 6 \left(- 3\right) + 1 = 9 - 18 + 1 = - 8$

Stationary point occurs at $\left(- 3 , - 8\right)$