f(x)= sinx+ 3^1/2cosx is max when x=?

if i solve it lyk...divide eqn by 2 and it converts to 2sin(pi/6+x)

thus it is max when x= pi/3 as sin is max at pi/2

and if i apply maxima minima...ans is pi/6

wat is the mistake in this?

here pi is 3.14

Dear SHEFALI,

As you calculated:

2sin(pi/6+x) is maximum when (pi/6+x)=pi/2 or x=pi/3.

Also by maxima minima f(x)=2sin(pi/6+x)

differentiating we get f'(x)=2cos(pi/6+x) and equating equal =0

Thus (pi/6+x)=pi/2

solving we get x=pi/3

Also we can check here whether at x=pi/3 we are getting maxima or minima.

double differentiating f(x) we get f''(x)=-2sin(pi/6+x)

Putting x=pi/3 here we get f''(x)=-2 which is less than 0.Thus at x=pi/3 f(x) is having a maxima.

Thus we are getting the same value of x as pi/3 by both of the ways.

And about the value of pi.

pi radians =180degree.Value of pi is 22/7=3.14.

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.

All the best STUDENT NAME !!!

Regards,

Askiitians Experts

MOHIT