show that the function f(x)= sin (2x+ pie/4) is decreasing in 3pie/8 x 5 pie/8 - Maths - Application of Derivatives

Question

show that the function f(x)= sin (2x+ pie/4) is decreasing in
3pie/8 <x<5 pie/8

Neha Sethi · Accepted Answer

Dear student
We have,f(x)=sin2x+π4f'(x)=2cos2x+π4Here,3π8<x<π5π8⇒3π4<2x<π5π4⇒π<2x+π4<3π2⇒cos2x+π4<0    ∵cos function is negative in third quadrant⇒2cos2x+π4<0⇒f'(x)<0 ,∀x∈3π8,5π8So, f(x) is decreasing on 3π8,5π8
Regards

show that the function f(x)= sin (2x+ pie/4) is decreasing in 3pie/8 <x<5 pie/8