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Calculus · Extrema

Critical points of x^2 + 16/x

x^{2} + \frac{16}{x}

Step by step

  1. f(x) = x^{2} + \frac{16}{x}

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

  2. f'(x) = 2 x - \frac{16}{x^{2}}

    Differentiate.

  3. x = 2

    Solve f′(x) = 0.

  4. f''(x) = 2 + \frac{32}{x^{3}}

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

  5. f''(2) = 6 \Rightarrow (2, 12) \text{ is a local minimum}

Reveal the answer
(2, 12)\ \text{local minimum}