Mathematics · Calculus
If a differentiable function f(x) has a local maximum at a point x = c, then which of the following conditions must be satisfied?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f'(c) = 0 and f''(c) < 0
- 2f'(c) = 0 and f''(c) > 0
- 3f'(c) ≠ 0 and f''(c) = 0✓
- 4f'(c) = 0 and f''(c) = 0 always
Correct answer
f'(c) ≠ 0 and f''(c) = 0
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