GATE CE 2025 Set 2 — Question 44
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Engineering Mathematics → Calculus → Local Maxima & Minima
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Question
Consider the function given below and pick one or more CORRECT statement(s) from the following choices.
Correct answer
(A) f(x) has a local minimum at x = 3.; (D) f(x) has a local maximum at x = 2.
Solution
Given .
First derivative: .
Setting . Critical points are and .
Second derivative: .
At . Thus, has a local maximum at .
At . Thus, has a local minimum at .
First derivative: .
Setting . Critical points are and .
Second derivative: .
At . Thus, has a local maximum at .
At . Thus, has a local minimum at .
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