दिखाई की `x=(pi)/(3)`पर `sin x (1+cos x )` का मान महत्तम है |

Explanation

माना की `y= sin x (1+ cos x )" "...(i)`
` therefore " "(dy)/(dx) =cos x ( 1+cos x )+sin x (-sin x )=cos x + (cos ^(2) x -sin ^(2) x)`
` " " =cos x + cos 2x `
`therefore " "(d^(2)y)/(dx^(2))=-sin x- 2sin 2x " "...(3)` ltBrgt (2 )से ` x =(pi)/(3) ` पर `(dy)/(dx) =cos ""(pi)/(3) +cos ""(2pi)/(3) =(1)/(2) -(1)/(2) =0`
` (3) ` से, ` x= (pi)/(3) ` पर ` (d^(2)y)/(dx^(2)) =-sin""(pi)/(3)-2sin ""(2pi)/(3)`
` " "= -(sqrt(3))/(2) - 2 (sqrt(3))/(2) =(-3sqrt(3))/(2) lt 0`
अतः y का मान `x= (pi)/(3)` पर महत्तम है