Came accross interesting problem in some GATE computer science paper.

Consider the function f(x) = sin (x) in the interval x ∈ [π/4, 7π/4]. The number and location(s) of

the local minima of this function are

(A) One, at π/2

(B) One, at 3π/2

(C) Two, at π/2 and 3π/2

(D) Two, at π/4 and 3π/2

Was quick to answer (B). Here is the plot of the graph, one of the minima is clearly 3π/2. However, in this case π/4 is a local minimum too (definitely clearer if we draw the function just within the ranges). **So the answer is (D).**

Note that this is only true when the interval is closed i.e. including points π/4 and 7π/4. If the problem was x ∈ (π/4, 7π/4) then π/4 is NOT a local minima as its NOT part of the function domain. Also, no matter what point we pick close to π/4 as our local minimum there will be a number lower than that. In that case this function would have just one minimum at 3π/2.

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