Question

find the maximum and minimum values of the function F X equal to sin x(1 + cosx )in the interval [0,2pi]​

Answer 1

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Class 12

>>Maths

>>Application of Derivatives

>>Maxima and Minima

>>f(x) = sin x (1 + cosx) has maximum valu

Question

Bookmark

f(x) = sin x (1 + cosx) has maximum value at x=

Easy

Solution

verified

Verified by Toppr

Correct option is C)

f(x)=sinx(1+cosx)

f(x)=sinx+

2

1

sin2x

On differentiating w.r.t x, we get

f

′

(x)=cosx+cos2x

Therefore,

cosx+2cos

2

x−1=0

2cos

2

x+cosx−1=0

2cos

2

x+2cosx−cosx−1=0

(2cosx−1)(cosx+1)=0

cosx=−1orcosx=

2

1

Clearlymaximumoccursatx=

3

π