Finbd the average rate of change for the function over the given interval

f(x) = x^3 + 1
[2,3]

Question

Finbd the average rate of change for the function over the given interval

f(x) = x^3 + 1
[2,3]

anonymous · Answer

First plug in your x-values of your interval to find the points the function goes through.
2^3+1 = 9 , so (2,9)
3^3+1 = 28 , so (3,28)

Now "rate of change" is the definition of slope. So use the slope formula to find the answer:

$$m=\frac{ y2-y1 }{ x2-x1 } = \frac{ 28-9 }{ 3-2 } = \frac{ 19 }{ 1 } = 19$$
The rate of change is 19.

anonymous · Answer

Ah that makes so much more sense than what the teacher gave us. Thanks.

anonymous · Answer

I should ask though, because I could have misread the question, is this supposed to deal with derivatives? Have you been doing derivatives in class?

anonymous · Answer

No, we're still on limits. You got it right,the back says 19, I just wasn't sure how to get it.

anonymous · Answer

Oh, okay I'm glad then. Sometimes "rate of change" refers to the derivative so you would find the derivative at both points x=2 and x=3 then divide by 2 for the average. I'm actually curious if that'd give the same answer.. But either way, glad I could help!