Find the average rate of change for f(x) = x^2
from x = delta(x) to x = x + delta(x).
USE delta(y)/delta(x) = [f(b) - f(a)]/(b - a)
You are just being asked to find the slope of some secant line on the function. It looks like you can probably just pick whatever points on the graph that you want. So, you know this parabola goes through (1,1) AKA (a, f(a)) Find another point on the graph to use for your "b" and then work it out. Not sure what your question is. Hope that helps!
SLOPE-AVERAGE RATE OF CHANGE.doc
It is a parabola with its vertex at the origin. "a" & "b" are x-values somewhere on the graph. f(a) and f(b) are the y-values associated with those x-values.
The average rate of change of a function is the slope of a secant line of the function. A secant line is a straight line that goes through the graph of the function intersecting at two separate points.
The slope of the secant line is:
So, choose any value of x, let's say x=2. Now, to find the y-value associated with that x-value, plug the x-value into your function.
which can also be written as
So when x=2 on the graph of this function, y=4
Does that make sense?
a = 2
f(2) = 4
Now pick another value on your function, let's say x = -1
Plug -1 into , you get
b = -1
f(b) = 1
So from your problem:
So, the average slope of your function is m = 1
Does that help you understand now?