GATE_AE_2027_MOCK_05_Q13
GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale)
MCQ · 1 Mark
Engineering Mathematics • Calculus • Maxima, Minima & Saddle Points
For a single-variable differentiable function f(x), if f'(c) = 0 and f''(c) < 0, then the point x = c is:
(A) A local maximum
(B) A local minimum
(C) An inflection point
(D) A discontinuity
Answer Key:
A
Step-by-Step Verified Solution
### Solution: By the second derivative test, f'(c) = 0 with f''(c) < 0 indicates the curve is concave down, hence x = c is a local maximum. Correct: A.