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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


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

Grade:12

1 Answers

Askiitians Expert Mohit Singla
19 Points
10 years ago

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.

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