Question

In two or more complete sentences, explain how to find the interval(s) in which the function f(x) is decreasing and how interval notation is used to
express the interval(s). In your final answer, include the interval in which the function is decreasing.

I tried doing the question and got this. *When there's a slope, that means it's decreasing. The point before the dip is the interval, meaning that it is (4,4).*
My teacher told me I was on the right track, but didn't get it right. I'm not very good at this stuff.

Graph: https://us-static.z-dn.net/files/d71/44c78f0be500a1b4d84afd3d62a5f

Answer 1

A function is said to be decreasing when it has a negative slope.
In calculus terms:
f(x) is decreasing when f'(x) < 0.

Answer 2

I still don't understand.

Answer 3

Did I get the interval right?

Answer 4

One thing at a time, please. You need to identify the interval or intervals on which the slope is positive and the interval or intervals on which the slope is negative. Your "when there is a slope, it's decreasing" is inaccurate, because you left out the word "negative," and your "it's" is vague. Instead: "when the slope is neg, the function is decreasing; when the slope is pos., the function is increasing."

Identify one interval on which the slope is positive, please.

Answer 5

Your link does not work for me.
This drawing might help you however.

The gradient function f'(x) is negative over the interval.