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Find the maximum value of the function f(x) = 1 + 2 sin x + 3 cos^2 (x) ; [0,2p/3] i want caluclations

Find the maximum value of the function f(x) = 1 + 2 sin x + 3 cos^2 (x) ; [0,2p/3]
i want caluclations

Grade:12th pass

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
f'(x)=2cosx-6cosxsinx=0
2cosx(1-3sinx)=0
cosx=0 or sin(x)=1 f(x)=1+2=3
sinx=1/3 imply cos^2(x)=1-1/9=8/9

f(x)=1+2/3+3*8/9=1+10/3=4.33
hence answer is 4.33.


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