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ਕਦਮ ਦਰ ਕਦਮ

1. f(x) = x^{4} - 2 x^{2}

   Critical points are where f′(x) = 0 or is undefined.

2. f'(x) = 4 x^{3} - 4 x

   Differentiate.

3. x = -1, x = 0, x = 1

   Solve f′(x) = 0.

4. f''(x) = 12 x^{2} - 4

   Second-derivative test: f″ < 0 → maximum, f″ > 0 → minimum.

5. f''(-1) = 8 \Rightarrow (-1, -1) \text{ is a local minimum}

6. f''(0) = -4 \Rightarrow (0, 0) \text{ is a local maximum}

7. f''(1) = 8 \Rightarrow (1, -1) \text{ is a local minimum}