I’m attempting to sketch the graph of the following question, how would I answer the interval chart steps below?

Question

Info:

1. the interval is for the following function,

y = cos(2x)

—————-

3-2sin²(x)

1. I’m sketching the graph of it
2. dy/dx can only be positive or negative
3. slope can only be up or down
4. Im confused as to if the interval would be positive or negative for the following function because it has alot of curves

1. what’s the dy/dx or slope of -2pi < x < pi/2 ?
2. what’s the dy/dx or slope of pi/2 < x < 3pi/2 ?
3. what’s the dy/dx or slope of 3pi/2 < x < 2pi ?

Answer 1

Hot tip. Go to desmos.com and graph it. It really helps to see graphs and check your answers. You can click on zeros of the function and min/max as well.

The graph shows that dy/dx >0 from pi/2 to pi and 3pi/2 to 2pi

It has dy/dx < 0 from 0 to pi/2 and pi to 3pi/2