Determine all critical points for the function.
-$$f ( x ) = 20 x ^ { 3 } - 3 x ^ { 5 }$$
A) $x = 2$
B) $x = - 2$
C) $x = - 2$ and $x = 2$
D) $x = 0 , x = - 2$, and $x = 2$

Question

Quizplus · Accepted Answer

To find the critical points, first find the derivative of the function: $f'(x) = 60x^2 - 15x^4$. Setting this equal to zero gives $60x^2 - 15x^4 = 0$, which simplifies to $15x^2(4 - x^2) = 0$. This equation has solutions at $x = 0$, $x = 2$, and $x = -2$, making them the critical points of the function.

Determine All Critical Points for the Function f(x)=20x3−3x5f ( x ) = 20 x ^ { 3 } - 3 x ^ { 5 }f(x)=20x3−3x5

Determine All Critical Points for the Function $f ( x ) = 20 x ^ { 3 } - 3 x ^ { 5 }$