GATE EE 2014 Set 1 — Question 12
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
Let . The maximum value of the function in the interval is
Correct answer
(A) e⁻¹
Solution
To find the maximum value of :
1.Find the first derivative: .
2.Set to find critical points: (since ).
3.Check the second derivative: .
4.Evaluate : . Since the second derivative is negative, is a point of local maximum.
5.The maximum value is .
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