Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3.

Question

Robin Chourasia · Answer

y= 1 + 2 sin x + 3 cos2x

y'= 2 cos x -6 sin 2x

y''= -2sinx-12cos2x

from y' we get,

2 cos x(1-6sinx)=0

=> x=90 or sin x= 1/6

y'' at x= 90 we get y'' = -2 - 12 (-1) = 10

at sinx = 1/6 we get y'' = -2 *1/6 -12 (1- 1/18)= -1/3- 34/3 =-35/3

Substituting both values in Y we get, @ x = 90 y = 0 @ sinx = 1/6 y = 1+ 1/3 + 3 (1-1/18)= 25/6 is maximum value..

Regards,

Robin

askiitian faculty

Parvez ali · Answer

Thanks & Regards Parvez Ali askIITians Faculty

Sher Mohammad · Answer

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. Sher Mohammad B.Tech, IIT Delhi.

bharat bajaj · Answer

f(x)= -3sin 2 x + 2sinx + 4 = -3(sin 2 x-2/3 sinx)+ =-3(sinx-1/3)^2+3/9+4 =-3(sinx - 1/3)+13/3 Now, for f(x) to be max, the first term should be minimum. Hence it is at sin x =0 Hence, max. value of f(x) = 16/3 Thanks & Regards Bharat Bajaj askIITians Faculty IIT Delhi

bharat bajaj · Answer

f(x)= -3sin 2 x + 2sinx + 4 = -3(sin 2 x-2/3 sinx)+ =-3(sinx-1/3)^2+3/9+4 =-3(sinx - 1/3)+13/3 Now, for f(x) to be max, the first term should be minimum. Hence it is at sin x =0 Hence, max. value of f(x) = 16/3 Thanks & Regards Bharat Bajaj askIITians Faculty IIT Delhi

Sunil Kumar FP · Answer

thanks and regards sunil kr askIItian faculty

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Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3.

Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3.

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