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For what value of , the function f(x)=sinx+1/2cos2x attains its absolute maximum in [0 ,pi/2]?

For what value of , the function f(x)=sinx+1/2cos2x
attains its absolute maximum in
[0 ,pi/2]?

Grade:12th pass

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
Differentiate f(x),
f`(x) = cos x - sin 2x = 0
cos x = 2 sin x cos x
sin x = 1/2
x = 30 degrees
f``(x) = -sin x - 2cos2x which is negative at x = 30. Hence, it is a maximum
f(x) = 1/2 + 1/4 = 3/4 at x = 30
THanks
Bharat Bajaj
IIT Delhi
askiitians faculty

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