Mathematics · Convex Analysis
Suppose that f : &mathbb;Rn → &mathbb;R, n ≤ 2 is a C2 function satisfying f(y) ≥ f(x) + ∇f(x)(y − x) for every x, y in &mathbb;Rn, where ∇ denotes the gradient. Which of the following statements is always true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is constant if f is bounded.
- 2f is convex and bounded.
- 3f is convex.✓
- 4f is constant.
Correct answer
f is convex.
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