GATE EC 2022 Set 1 — Question 36
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
The function attains its minimum over the interval at _________.(Here is the natural logarithm of .)
Correct answer
(B) 1
Solution
To find the minimum of on the interval :
Set (since and ).
At , . Thus, is a local maximum.
Comparing and , the minimum value is 2, which occurs at .
1.Find critical points:
Set (since and ).
2.Check the nature of the critical point:
At , . Thus, is a local maximum.
3.Evaluate at boundaries:
Since there is only one local maximum in the interval, the minimum must occur at one of the endpoints.Comparing and , the minimum value is 2, which occurs at .
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