Answer:
C.N x = ±√2, 0
Step-by-step explanation:
Basic Power Rule:
f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹
Critical numbers occur when f'(x) is equal to zero or undefined.
Step 1: Define function
f(x) = x⁴ - 4x²
Step 2: Find critical numbers
- Find derivative of f(x): f'(x) = 4x³ - 8x
- First Derivative Test: 0 = f'(x)
- First Derivative Test: 0 = 4x³ - 8x
- Factor and Solve: 0 = 4x(x² - 2)
- Critical Numbers: x = ±√2, 0
