GATE CS 2015 Set 2 — Question 5
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Engineering Mathematics → Calculus → Maxima & Minima
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Question
Consider a function on . The value of at which the function attains a maximum, and the maximum value of the function are:
Correct answer
(C) 0, 1
Solution
The given function is defined on the interval .To find the maximum value of , we need to minimize .
The absolute value function is always non-negative, i.e., .
The minimum value of occurs at , where .Since is within the given interval , the minimum value of in this interval is at .Substituting into the function:
.This is the maximum value of because will be largest when is smallest.So, the function attains its maximum value of at .Comparing this with the given options:
(A) (x value, max value)
(B) (x value, max value)
(C) (x value, max value)
(D) (x value, max value)The correct option is (C).The final answer is
The absolute value function is always non-negative, i.e., .
The minimum value of occurs at , where .Since is within the given interval , the minimum value of in this interval is at .Substituting into the function:
.This is the maximum value of because will be largest when is smallest.So, the function attains its maximum value of at .Comparing this with the given options:
(A) (x value, max value)
(B) (x value, max value)
(C) (x value, max value)
(D) (x value, max value)The correct option is (C).The final answer is
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