Question

Find all relative minima of the given function y = x⁴ - 8x³.

A) x = 0
B) x = 2
C) x = -2
D) x = 4

Answer 1

To find the relative minima of the function y = x⁴ - 8x³, we need to find the derivative, set it equal to zero, and solve for x. The relative minima of the function are x = 0 and x = 6.

Step-by-step explanation:

To find the relative minima of the function y = x⁴ - 8x³, we need to first find the derivative of the function and then find where the derivative equals zero.

Step 1: Find the derivative of y = x⁴ - 8x³.

The derivative of y = x⁴ is 4x³, and the derivative of y = -8x³ is -24x². So, the derivative of y = x⁴ - 8x³ is 4x³ - 24x².

Step 2: Set the derivative equal to zero and solve for x.

4x³ - 24x² = 0

4x²(x - 6) = 0

x = 0 or x = 6

Thus, the relative minima of the function y = x⁴ - 8x³ are x = 0 and x = 6.