Let \(f:\mathbb{R}\to\mathbb{R}\) be a twice-differentiable function and…

GATE · 2025 · DA · Data Science & AI

Let f:R→Rf:\mathbb{R}\to\mathbb{R} be a twice-differentiable function and suppose its second derivative satisfies f′′(x)>0f''(x)>0 for all x∈Rx\in\mathbb{R}. Which of the following statements is/are ALWAYS correct?

  1. A.

    f has a local minima

  2. B.

    There does not exist xx and yy, x≠yx\ne y, such that f′(x)=f′(y)=0f'(x)=f'(y)=0

  3. C.

    f has at most one global minimum

  4. D.

    f has at most one local minimum

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