GATE 2012 CS (CS1) – Question 19
For f(x)=sin x on [π/4,7π/4], find the local minima and their locations.
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Correct answer: (D) Two at π/4 and 3π/2
Explanation
Within the interior, sin x has a minimum at 3π/2 and a maximum at π/2. Relative to the restricted closed interval, the left endpoint π/4 is also a one-sided local minimum because the function increases immediately to its right. The official convention counts both, D. Excluding endpoint extrema would give B.