GATE DA 2025 Set 1 — Question 49
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Calculus & Optimization → Maxima, Minima & Optimization → Single Variable Optimization
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Question
Consider the function , . Which of the following statements is/are correct?
Correct answer
(C) The maximum value of f is (133)/(2); (D) The minimum value of the derivative of f is attained at x = -(7)/(2)
Solution
The derivative is . Critical points are . The domain is .
Evaluating at critical points and endpoints:
The maximum value is at . Thus, option (C) is correct and (A) is incorrect.
The minimum value is at . Thus, option (B) is incorrect.The derivative is a parabola opening upwards with vertex at . Since , the minimum of the derivative is attained at . Thus, option (D) is correct.
Evaluating at critical points and endpoints:
The maximum value is at . Thus, option (C) is correct and (A) is incorrect.
The minimum value is at . Thus, option (B) is incorrect.The derivative is a parabola opening upwards with vertex at . Since , the minimum of the derivative is attained at . Thus, option (D) is correct.
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