GATE DA 2024 Set 1 — Question 50
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Calculus & Optimization → Maxima, Minima & Optimization → Single Variable Optimization
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Question
Consider the function where is the set of all real numbers.Which of the following statements is/are TRUE?
Correct answer
(A) x = 0 is a local maximum of f; (B) x = 3 is a local minimum of f
Solution
First, find the first derivative :Set to find critical points: .Next, find the second derivative :Evaluate at each critical point:
(A) is a local maximum. (True)
(B) is a local minimum. (True)
(C) is a local maximum. (False, it is a minimum)
(D) is a local minimum. (False, it is a maximum)Correct options are (A) and (B).
1.At : Local Maximum.
2.At : Local Minimum.
3.At : Local Minimum.
Checking the options:(A) is a local maximum. (True)
(B) is a local minimum. (True)
(C) is a local maximum. (False, it is a minimum)
(D) is a local minimum. (False, it is a maximum)Correct options are (A) and (B).
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