For the given function, find the critical numbers. $y = \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 3 } } { 3 } - 4$
A) $x = 0 \text { and } x = 1$
B) $x = 0 \text { and } x = 4$
C) $x = 0 \text { and } x = - 4$
D) $x = 0 \text { and } x = - 1$
E) $x = - 1 \text { and } x = 1$

Question

Quizplus · Accepted Answer

To find the critical numbers, first find the derivative of the function: $y' = x^3 - x^2$. Setting the derivative equal to zero gives $x^3 - x^2 = 0$, which factors to $x^2(x - 1) = 0$. This gives critical numbers at $x = 0$ and $x = 1$.

For the Given Function, Find the Critical Numbers y=x44−x33−4y = \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 3 } } { 3 } - 4y=4x4​−3x3​−4

For the Given Function, Find the Critical Numbers $y = \frac { x ^ { 4 } } { 4 } - \frac { x ^ { 3 } } { 3 } - 4$