show that has a root on [1,2]
use the two steps of the crossing method that contains the root.
find the root of the equation using newton referson methos.
solution of the book:
so it rises and the is no root in [0,pi/3] interval
then they say that in [pi/3,pi] f(x) going down because f'(x)<0
so there is a solution in this interval
but how does f'(x)<0 shows that there is a soltion??
in order to see that there is a solution we need to have two point one positive one negative and that f(x) is going down
why they check from 0 to pi
and not from [1,2] like asked in the question