How do I find the rate of change of a given function on a given interval?

Question

anonymous · Answer

the rate of change is the functions derivative.  dy/dx  

rate of change = "how fast is y changing based on the change in x"

anonymous · Answer

Ok, could you make that simpler? I'm in 8th grade taking a high school class, and my teacher hasn't really explained it enough, and I have a test tomorrow!

anonymous · Answer

are you asking about a particular function, or just any function in general?

anonymous · Answer

Any function in general.

anonymous · Answer

so the easiest way to do it would be to calculate y, or f(x) at two different x values

anonymous · Answer

so if you are given an interval, say 1 to 5

anonymous · Answer

calculate y at 1, and then y at 5

anonymous · Answer

then simply do (y5 - y1)/(5-1)

anonymous · Answer

or the change in y divided by the change in x

anonymous · Answer

Wow! Thanks! Could you by any chance give me an example problem, and let me do it and check me?

anonymous · Answer

yea.  say the function is f(x)=2x+1  from 0 to 4

anonymous · Answer

Ok. Wait a sec...

anonymous · Answer

Is it 2?

anonymous · Answer

(9-1)/(4-0) = 2

anonymous · Answer

Yes!!!

anonymous · Answer

Thank you soooooooooooooooooooooo much!!

anonymous · Answer

think of it as a slope or a hill, for every step you take forward, you will climb a certain amount.

anonymous · Answer

the steeper the slope, the higher the rate of change

anonymous · Answer

Ok. Thanks again!

By the way, I fanned you.