# Thread: average rate of change? help

1. ## average rate of change? help

average rate of change?

Problem:
Find the average rate of change of the function f(x)=-3(x^2)-x from x1=5 to x2=6. The formula for average rate of change from a to b is (f(b)-f(a))/b-a

a)-1/6
b)-34
c)-2
d)1/34
e)1/2

2. Hello!

All the information you need is given to you. You just need to plug it all in.

You are given your two x values (5 & 6) now, to find f(5) & f(6) just plug them into the function and find your y values.

f(x) = y

When you see f(x) that means that you are solving for y in terms of x

If you are given an x value and a function f(x), you can plug the x value into every single x in the function and it will calculate the y value associated with that x value. So f(5) = -80 See if you can go from there!
Good Luck!

3. Originally Posted by mollymcf2009
Hello!

All the information you need is given to you. You just need to plug it all in.

You are given your two x values (5 & 6) now, to find f(5) & f(6) just plug them into the function and find your y values.

f(x) = y

When you see f(x) that means that you are solving for y in terms of x

If you are given an x value and a function f(x), you can plug the x value into every single x in the function and it will calculate the y value associated with that x value. So f(5) = -80 See if you can go from there!
Good Luck!

huh? i think i am more confused than before...........

4. Ok, no problem. Let me try to explain it another way.

The average rate of change of a function is also known as the slope. You know what slope is right?

slope = $\frac{y_2-y_1}{x_2-x_1}$

OR,

slope = $\frac{change-in-y-values}{change-in-x-values}$

OR,

slope = $\frac{f(b)-f(a)}{b-a}$

b & a are just x coordinates somewhere on your function

f(b) & f(a) are the y values associated with those x values.

Since you are given the x values of the coordinates on the function, just plug those into your function to give you the y values.

All that f(x) means is y. f(x) is the function y, evaluated at an x value.

So for example:

$f(x) = 2x^2 - 6x + 3$

Find f(2).

$f(2) = 2(2)^2 - 6(2) + 3$

In calculus,

The average rate of change of a function is the slope of the of the secant line between two points somewhere on the graph. A secant line is a line that goes through the graph of a function in two places. It calculates the average of the slopes of all the tangent line to the function between those two given points.

Hope that clarifies better for you

5. yea i got it now.
thank you so much