# How do you find the critical points for f(x)=-x^2+6x+2?

$x = 3$

#### Explanation:

Given polynomial function:

$f \left(x\right) = - {x}^{2} + 6 x + 2$

$f ' \left(x\right) = - 2 x + 6$

$f ' ' \left(x\right) = - 2$

for critical (minima or maxima) points $f ' \left(x\right) = 0$, hence

$- 2 x + 6 = 0$

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

$x = 3$

since $f ' ' \left(x\right) = - 2 < 0$ hence the function is maximum at $x = 3$