Question

What is the rate of change for the interval between A and B?

Answer 1

I believe it's 0

Answer 2

Why do you believe it's zero?

Answer 3

the first line is on the negative 2 while the second is on the postive 2 vertically. so that equals 0 @TurtleMuffin

Answer 4

The question is asking for the rate of change between A and B.

That is, by how much did the graph change between A and B?

Immediately we should see that the point B is higher than point A, so clearly the change between A and B is positive! So the rate of change cannot be zero.

So how do we find the rate of change. We look at the change in the vertical direction, and divide that by the change in the horizontal direction. In other words, rise over run. In other words, slope. What's the slope between those two points?

Answer 5

@TurtleMuffin the slop is 2

Answer 6

take the first derivative of the function then evaluate f('x) at B - f'(x) at A

Answer 7

@triciaal I understood I total of 2 words in that sentence, How do I evaluate f(x)?

Answer 8

what are you saying?

Answer 9

what I said was find the function then take the derivative
evaluate at the point b and evaluate at the point a (using the x-values)
change means difference
change in slope means difference in slope
subtract the 2 values

Answer 10

of course this is only one approach

Answer 11

remember the first derivative of the function is the slope

Answer 12

the slope is the rate of change

Answer 13

Is there anything from my response you really don't understand?

Answer 14

the rate of change is: \[\frac{f(2)-f(1)}{2-1}=\frac{1-(-2)}{1}\]

Answer 15

@triciaal so I just need to find the slope?

Answer 16

yes the slope is the rate of change between A and B

Answer 17

@xapproachesinfinity @triciaal Alright, thank you both for your help, I'm gonna go brush up my knowlege and re-look at that section in my textbook

Answer 18

No problem :)

Answer 19

welcome