Find the intervals in which the function f given by
f(x)=sinx + cosx ,o≤x≤2pi is strictly increasing or strictly decreasing

Question

Find the intervals in which the function f given by 
f(x)=sinx + cosx ,o≤x≤2pi is strictly increasing or strictly decreasing

diyadiya · Answer

$$f(x)=sinx+cosx$$
$$f'(x)=cosx-sinx$$

anonymous · Answer

okay, then if you want you can continue with the second derivative test

diyadiya · Answer

Hm ok
if sinx=cosx then what are the values of x?

anonymous · Answer

From the unit circle pi/4 and 5pi/4

anonymous · Answer

I think it can be best done by second derivative method !!!

diyadiya · Answer

Can you show ?

anonymous · Answer

for strictly increasing we should do double derivative.so,by that we'll get -(sinx+cosx)
modifying it -sqrt(2)sin(x+pi/4).so it is strictly increasing in (0,pi/4) & strictly decreasing in (pi/4,5pi/4)