Flag Integral Calculus> f(x)=1+2sin x+3cos ²x[0,2p÷3]FIND MAX VAL...
question mark

f(x)=1+2sin x+3cos ²x[0,2p÷3] FIND MAX VALUE OF FUNCTION

naveen , 11 Years ago
Grade upto college level
anser 2 Answers
Sunil Raikwar

Last Activity: 11 Years ago

Let y = 1+2sinx+3cos2x

Differentiate with respect to x
y' = 2cosx-6cosxsinx or 2cosx-3sin2x
put y' = 0
cosx(1-3sinx) = 0
cosx = 0, sinx = 1/3
again Diffentiate with respect to x
y'' = -2sinx-6cos2x
y'' greater than zero for cosx=0 & less than zero for sinx=1/3
hence y give maximum value at sinx=1/3
maximum value of y= 1+ 2/3+ 3*2/9=5/3

Sunil Raikwar

Last Activity: 11 Years ago

Let y = 1+2sinx+3cos2x
Differentiate with respect to x
y' = 2cosx-6cosxsinx or 2cosx-3sin2x
put y' = 0
cosx(1-3sinx) = 0
cosx = 0, sinx = 1/3
again Diffentiate with respect to x
y'' = -2sinx-6cos2x
y'' greater than zero for cosx=0 & less than zero (negative) for sinx=1/3
hence y give maximum value at sinx=1/3
maximum value of y= 1+ 2/3+ 3*2/9=5/3

Thanks & Regards
Sunil Raikwar
askIITians faculty

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free