Average Rate of Change

[kat2071]

I am to find the Average Rate of Change (AROC) for the following equation f(x)= 3cosx-1 in the restrictions [pie/4, 7pie/4]

I have tried plugging everything into the formula my professor gave today that f(x+h)-f(x) / h will equal the AROC

In class h was always 0.1, 0.01, and 0.001.

my problem is that in class, we neither covered how to do this when cosine was involved nor what to do when there is a umber before x in the equation!

 

[mmm4444bot]

I have tried plugging everything into the formula … f(x+h)-f(x) / h

I can't see your work. Maybe you're making it more difficult than it needs to be.

cos(?/4) = cos(7?/4)

Therefore, f(x + h) and f(x) are the same number. In other words, the function ends up where it started across the given interval, so the average rate by which the function changes over that interval must be zero.

We arrive at the same conclusion, when we use the formula.

It helps to realize that the Average Rate of Change (AROC) is the slope of a line connecting two points on the graph of y = 3*cos(x) - 1. Specifically, these two points are where x = ?/4 and x = 7?/4.

:?: Do you know how to find the slope of a line through two points using coordinates ?

m = (y2 - y1)/(x2 - x1)

The formula that you posted shows the same relationship; only the symbols are different.

AROC = [ f(x + h) - f(x) ] / h

AROC is just another way of writing m

f(x + h) is another way of writing y2

f(x) is another way of writing y1

h is another way of writing x2 - x1

Determining the values on the righthand side of the formula and plugging them in to find the slope is all that you need to do, in this exercise.

Again, here are the three numbers you need to calculate:

h

f(x)

f(x + h)

The value for h is the amount by which x changes moving from x = ?/4 to x = 7?/4.

:?: Tell me, what is the distance from ?/4 to 7?/4 ?

Next, you need to determine the y-coordinate of each point; they are f(x + h) and f(x).

The variable x is ?/4 in this exercise. So f(x) is f(?/4).

Evaluate f(?/4) using the given definition for function f.

f(?/4) = 3*cos(?/4) - 1

To evaluate f(x + h), we use the fact that x + h = 7?/4 in this exercise.

Evaluate f(7?/4) = 3*cos(7?/4) - 1

Once you have all three numbers, do the arithmetic to evaluate the slope [f(x + h) - f(x)]/h.

If you want more help from me, you must respond to my questions and show whatever work you can so that I can see what you're doing.

Please, feel free to ask specific questions about anything that you do not understand.