# Intervals of increase and decrease

• Apr 11th 2009, 11:27 AM
justin016
Intervals of increase and decrease
interval -pi<=x<=pi
y=cosx-sinx
dy/dx= -sinx-cosx
sinx=-cosx
cosx=-sinx
tanx=-1
two angles are -pi/4 and 3pi/4

I am stuck here. Normally i would use a table to determine the period of increase and decrease from y'. How do you set up the table in this case?
• Apr 11th 2009, 11:42 AM
Calculus26
use a graph
Set up a graph for the derivative -sin(x) -cos(x) on (-pi,pi)

you already know the zeroes--so just look where the graph is positive

If you must use a table consider -pi to pi/4, -pi/4 to 3pi/4 and 3pi/4 to pi
• Apr 11th 2009, 11:43 AM
skeeter
Quote:

Originally Posted by justin016
interval -pi<=x<=pi
y=cosx-sinx
dy/dx= -sinx-cosx
sinx=-cosx
cosx=-sinx
tanx=-1
two angles are -pi/4 and 3pi/4

I am stuck here. Normally i would use a table to determine the period of increase and decrease from y'. How do you set up the table in this case?

[-pi ............-pi/4..............3pi/4.............pi]

pick a value in each interval, and determine the sign of y' in that interval.

first interval, y'(-pi) > 0 ... y is increasing

second interval, y'(0) < 0 ... y is decreasing

third interval, y'(pi) > 0 ... y is increasing