The function f(x) = x + cos x has:
The function f(x) = x + cos x has:
- A. No local maxima or minima
- B. A local maximum
- C. A local minimum
- D. Both local max and min
Answer: A) No local maxima or minima
Explanation: f'(x) = 1 − sin x. Since sin x ≤ 1, f'(x) ≥ 0 for all x, and f'(x) = 0 only at isolated points x = π/2 + 2nπ. Hence f is strictly increasing and has no local extrema.
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