Question

Find the sub-interval of `(0,pi/2)` in which f(x) = log (sin x + cos x) is increasing and decreasing.

Answer 1

F'(x) = `1/(1+(sinx+cosx))(cosx-sinx)`

Put F'(x) = 0

⇒ `(cosx-sinx)/(1+sinx+cosx)=0`

⇒ cosx – sinx = 0

⇒ cosx = sinx

⇒ `1=sinx/cosx`

tan x = 1

x = `pi/4`

Increasing `(0,pi/4)`

Decreasing `(pi/4,pi/2)`