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Find the maximum value of the function f(x) = 1 + 2 sin x + 3 cos2 x ; 0 >= x >= 2/3

Find the maximum value of the function f(x) = 1 + 2 sin x + 3 cos2 x ; 0 >= x >= 2/3

Grade:11

1 Answers

ruchi yadav
askIITians Faculty 27 Points
7 years ago
In the given question because there is limit on x also so cannt calculate range directly .
So first differentiating the function we get cosx = o or sinx =1/6.
So between these two points we get maximum at sinx = 1/6


so putting value sinx = 1/6 we get,

1+2/6+3( 1-2(1/36))
= 25/6

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