GATE EC 2014 Set 2 — Question 13
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
For , the maximum value of the function occurs at
Correct answer
(A) t = ₑ 4
Solution
To find the maximum value of , we first find its derivative with respect to and set it to zero:Setting :Dividing by (which is never zero):Taking the natural logarithm on both sides:To verify it's a maximum, check the second derivative:At , and :Since the second derivative is negative, the function has a maximum at .
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