Question

Find all the critical numbers of the function f(x) = x^4 - 4x^2

Answer 1

C.N x = ±√2, 0

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

1. Find derivative of f(x): f'(x) = 4x³ - 8x
2. First Derivative Test: 0 = f'(x)
3. First Derivative Test: 0 = 4x³ - 8x
4. Factor and Solve: 0 = 4x(x² - 2)
5. Critical Numbers: x = ±√2, 0