Increasing and Decreasing Intervals

[john3j]

Hello,

I got through most of my homework but had skipped these two because I couldn't figure them out and my instructor is not responding to me. Sad thing is that the assignment is due tomorrow and my online instructor isn't responding. Anyhow, our book shows us . I see from this example how you can tell where the intervals increase and decrease when the letters are at the bottom, but I am having trouble understanding how to do and . I think that for number 6 here is what I think the answer is:

f is increasing on the intervals (-2, -infinity) and (-1, +infinity)
f is decreasing on the intervals (-2, 0).

I think that for number 10 is as follows:

f is increasing on the intervals (-4, -infinity), (-2, 1), and (5, +infinity)
f is decreasing on the intervals (-4, -2) and (1, 5)

Could someone please clarify for me? The instructions state that I need to "find the open intervals on which a. f is increasing and b. f is decreasing.

Thank you in advance.
John

 

[mmm4444bot]

I think that for number 6 here is what I think the answer is:

f is increasing on the intervals (-2, -infinity)

f is decreasing on the intervals (-2, 0).

Are you reading the graphs from left to right?

Also, interval notation requires writing the left boundary first, followed by the right boundary:

(-infinity, -2)

This notation describes all x-values less than -2.

But, to the left of x=-2, the graph of f is not going up. Why do you say f is increasing here?

 

[DrPhil]

View attachment 2488.

I think that for number 10 is as follows:

f is increasing on the intervals (-4, -infinity), (-2, 1), and (5, +infinity)
f is decreasing on the intervals (-4, -2) and (1, 5)

Could someone please clarify for me? The instructions state that I need to "find the open intervals on which a. f is increasing and b. f is decreasing.

Thank you in advance.
John

You have correctly found all the places where the slope is zero or undefined; however you made the same error that you made on #6: the proper way to write the first interval is from left-to-right:
(-infinity, -4)
What is the change of f(x) as you move from left to right?

Note that the sign of the slope does not necessarily change every time the slope is zero, as at x=-2. The open intervals on either side of x=-2 have the same sense.