GATE EE 2025 Set 1 — Question 11
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
Consider the set of points which minimize the real valued functionWhich of the following statements is true about the set ?
Correct answer
(B) The number of elements in the set S is infinite.
Solution
Let . The function can be rewritten as a function of a single variable :To find the minimum, we take the derivative with respect to and set it to zero:Since , this value of corresponds to a minimum. Thus, the function is minimized whenever .
The set represents a line in the 2D plane. A line contains an infinite number of points. Therefore, the number of elements in the set is infinite.
The set represents a line in the 2D plane. A line contains an infinite number of points. Therefore, the number of elements in the set is infinite.
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