Let y = −2x^3 + 3x^2 − 3.
Find and classify all critical points of y. Sketch the function, showing all important points.
Just wondering what the critical points are? Are the the max and min's of the function?
Cheers
Critical points, as Mr. Fantastic pointed out, include those values of x where f'(x)=0.
$\displaystyle f(x)=-2x^3+3x^2-3$
$\displaystyle f'(x)=-6x^2+6x$
$\displaystyle f'(c)=0$
$\displaystyle 0=-6c^2+6c$
$\displaystyle c={0,1}$
So, the critical points are (0,-3) and (1,-2).
It's not relevant for this particular function, but critical numbers also include those values of x where f(x)∈ℝ and f'(x) is undefined.