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## College Algebra

### Unit 10: Lesson 1

Average rate of change of polynomials

# Sign of average rate of change of polynomials

Finding the intervals where the polynomial h(x)=⅛x³-x² has a positive average rate of change.

## Want to join the conversation?

• I'm confused what it means when it Sal says that it should be `h(xf) > h(xi)` when all the answers are in a `a ≤ x ≤ b` format.

Also I'm not sure if Sal went over this in the video, but does having a negative number in `a` in `a ≤ x ≤ b` spot and a 0 or higher in the `b` spot mean it will be positive?
• The `h(xf) > h(xi)` is referring to `a ≤ x ≤ b`, where `h(xf)` is `b` and `h(xi)` is a.

Basically it is saying that in this situation for an answer to be correct, the output of `h(b)` has to be bigger than `h(a)` to warrant a positive change. If you were looking for a negative change it would be the other way around.

To answer your second question that might not always be the case.

Say you have `f(x) = -1x^2`

If the interval is `-1 ≤ x ≤ 1` then:

`f(-1) = -1` and `f(1) = -1`, making it not positive
• I don't understand any of this. I've watched the video numerous times and it still doesn't make sense. Can someone please help me?
• I'm not understanding the sign of interval change problem
problem A.) for example

h(x)=1/8 x^3-x^2
how did h(0)=0, h(2)=-3
• h(x) takes the place of y on an x-y plane, so when we're taking h(0), we're looking at the line the function makes and seeing what the number on the vertical axis is when the number on the horizontal axis is 0. In the equation, we're seeing what y (which is h(x)) is when x is 0. So we replace all the x's in the equation with 0, and then solve it. 0 · 1/8 is 0, and 0 to any exponent is also 0. So it ends up as 0 · 0, which is 0.
(1 vote)
• Just wondering... is there a faster way to do this than to go over all of the multiple choice options?
• Not really, it's kind of like guess and check in a way you have to go through each one individually
• When he is explaining problem C, 6^3 is 180. Where did he get the add 36 to get 216? Maybe I just missed it, but I am confused
• 6^3 is actually 216. When he says that 36 * 6 = (180 + 36) = 216, Sal is just breaking down the multiplication into parts that you could do mentally.
• i have a mid-term coming up and i have average rate of change on it and im definitely gonna fail because i dont get this at all. does anyone know a different video i can watch to understand better?
• you should look around for that on youtube using average rate of change as the search.
• How do you know which x value is the x final, and which x value is the x initial?
• Can someone explain to me the steps of how he is solving the answer choices, because he is going kind of fast?
• what does all this mean
what an average rate of change even is.
You can view it as, the change in your value of the function
for a given change in the underlying variable
for a given change in x?