GATE EE 2020 Set 1 — Question 36
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
For real numbers, and , with , the maximum and minimum value of for are respectively, ______.
Correct answer
(A) 7 and 1/4.
Solution
Given for .
To find the extrema, we first find the critical points by setting the derivative to zero:
.
Since , is a point of local minimum.
The value at the minimum is .
Next, we check the values at the endpoints of the interval :
At : .
At : .
Comparing these values, the maximum value is 7 and the minimum value is 1/4. Thus, option (A) is correct.
To find the extrema, we first find the critical points by setting the derivative to zero:
.
Since , is a point of local minimum.
The value at the minimum is .
Next, we check the values at the endpoints of the interval :
At : .
At : .
Comparing these values, the maximum value is 7 and the minimum value is 1/4. Thus, option (A) is correct.
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