Second derivative test

Calculus

Let f(x) be a differentiable function, and let (a, f(a)) be a critical point of f(x). Then,

1. If f”(a) > 0, then (a, f(a)) is a local minimum of f(x).

2. If f”(a) < 0, then (a, f(a)) is a local maximum of f(x).

3. If f”(a) = 0, then the second derivative test tells us nothing!

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