Question

Identify the open intervals where the function is increasing or decreasing.

Answer 1

So so you have to take a derivative of something to solve it? What do you have to do?

Answer 2

The sign of the 1st derivative tells us about the monotony of a function.

If the 1st derivative is strictly positive, then the function is strictly increasing and if the 1st derivative is strictly negative, then the function is strictly decreasing.

We'll differentiate the function with respect to x:

Answer 3

No you don't. Just look at the graph. Read it from left to right.
Where is that graph increasing...looking from left to right?

Answer 4

It's increasing from 0 to pi/2 and from 3pi/2 to 2pi

Answer 5

well it looks like it is increasing on 0 to pi/2

Answer 6

And indeed it is.

Answer 7

Which is not surprising given that the biggest that sin x term can be is 1 and that happens at pi/2

Answer 8

Increasing: (0, pi/2), (3pi/2 , 2pi)
Decreasing: (pi/2, 3pi/2)

Answer 9

it is decreasing on pi/2, 3pi/2? right?

Answer 10

that is correct.

Answer 11

haha! okay so I just have to look at the graph. That was way easier then I thought.

Answer 12

yep...not too bad

Answer 13

Thanks!