# How do you find the critical points to sketch the graph f(x)=7+6x-x^2?

Jun 12, 2017

$x = 3$

#### Explanation:

What you want to do first is find the derivative using the product rule:
Keep in mind that derivative of a constant is zero.

$f ' \left(x\right) = 0 + 6 - 2 x$

Then rearrange it and set it equal to zero:

$- 2 x + 6 = 0$

Solve it:

$- 2 x = - 6$

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

$x = 3$