Determine all critical points for the function.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2$$
A) x = 0 and x = 1
B) x = 0 and x = 2
C) x = -1 and x = 1
D) x = 0

Question

Quizplus · Accepted Answer

To find the critical points of the function $f(x) = x^3 - 3x^2 + 2$, we first need to find its derivative and then set that derivative equal to zero to solve for $x$. The derivative of $f(x)$ is $f'(x) = 3x^2 - 6x$. Setting $f'(x) = 0$ gives $3x^2 - 6x = 0$, which simplifies to $x^2 - 2x = 0$ or $x(x - 2) = 0$. This equation has solutions $x = 0$ and $x = 2$, which are the critical points of the function.

Determine All Critical Points for the Function f(x)=x3−3x2+2f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2f(x)=x3−3x2+2

Determine All Critical Points for the Function $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2$