# Find the critical numbers and stationary points of each of the following functions.$\;f(x)=2x-3x^{2}$

Note: This is part 1st of a 6 part question, split as 6 separate questions here.

Toolbox:
• A ciritical number of a function f is a number c in the domain of f such that either $f'(c)=0$ or $f'(c)$ does not exist.
• Stationary points correspond to critical numbers for which $f'(c)=0$
$f(x)=2x-3x^2$
Step 1:
$f'(x)=2-6x$
$f'(x)=0=>2-6x=0$
$x=\large\frac{1}{3}$ is a critical number
Step 2:
When $x=\large\frac{1}{3}, f( \frac{1}{3})=\frac{2}{3}-\frac{3}{9}=\frac{1}{3}$ (critical value)
The critical point is $(\large\frac{1}{3},\frac{1}{3})$