Question

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

Answer 1

\[f(x)=sinx+cosx\]
\[f'(x)=cosx-sinx\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Can you show ?

Answer 7

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)