Determine all critical points for the function.
-$$y = 4 x ^ { 2 } - 128 \sqrt { x }$$
A) x = 0
B) x = 4
C) x = 0, x = 4, and x = -4
D) x = 0 and x = 4

Question

Quizplus · Accepted Answer

To find critical points, we take the derivative of the function and set it equal to zero:
$$y' = 8x - \frac{128}{2\sqrt{x}} = 8x - 64x^{-\frac{1}{2}} = 0$$
Solving for x, we find x = 4 or x = 0. Therefore, the critical points are x = 0 and x = 4. Choice C is incorrect because -4 is not a critical point of the function.

Determine All Critical Points for the Function y=4x2−128xy = 4 x ^ { 2 } - 128 \sqrt { x }y=4x2−128x​

Determine All Critical Points for the Function $y = 4 x ^ { 2 } - 128 \sqrt { x }$