Question

Given f(x)=17-x^2 what is the average rate of change in f(x) over the interval [1, 5]?

Answer 1

the slope of the line that connects the endpoints ....

Answer 2

What do you mean by that? i dont understand

Answer 3

you find the slope of the line that connects the ends points

Answer 4

given 2 points, how do you find the slope of a line between them?

Answer 5

Don,t you count the sqaures?

Answer 6

Squares*

Answer 7

hmm, thats a graphical approach yes. which may or maynot be applicable here

Answer 8

There is no graph involved

Answer 9

if we go by the slope formula: lets find the change in y as it relates to the change in x\[slope:~\frac{y_1-y_o}{x_1-x_o}\]

Answer 10

in this case, we have our y parts as f(a) and f(b) for an interval from a to b

Answer 11

okay..

Answer 12

writing this down

Answer 13

with any luck it already written down in your course material

Answer 14

Well of course, but i never quite understood it. im trying to find an easier way to understand, which is why i came here.

Answer 15

there is no easier way to understand it. practice is the only way to make it understable

Answer 16

Okay, so in the equation would 17 be x?
to find the slope..

Answer 17

we know x1 and x2: 1 and 5, the endpoints of our interval

we want to know f(1) and f(5), which will be our y values to compare

Answer 18

the 17 part here is superfluous, but that might just confuse you at the moment

Answer 19

wait, are we subtracting?

Answer 20

yes, that will be the only way to find the difference between things, subtract them

Answer 21

\[slope:~~\frac{f(1)-f(5)}{1-5}\]

Answer 22

OH! the answer is 1?!

Answer 23

i doubt it

Answer 24

ughhh! i thought i had it.

Answer 25

we need to know the value of f(1) and f(5)

Answer 26

because i got negative 4 on top and bottom then i divided them and got 1

Answer 27

Okay

Answer 28

let me dbl chk

f(1) = 17-(1)^2
f(5) = 17-(5)^2

f(1) - f(5) is: 17-(1)^2 -(17-(5)^2) = -1+25

Answer 29

17-17 is 0 which is why a foretold that the 17 is really useless

Answer 30

so

\[\frac{f(1)-f(5)}{1-5}=\frac{-1+25}{-4}=\frac{24}{-4}\]

Answer 31

how did you get -1+25 on the top??

Answer 32

do you know what to do with a function? the f(x) that was defined?

Answer 33

I'm horrible at functions so no

Answer 34

well its really quite simple; lets name the equation as f(x), read 'f of x'.

lets give the name a definition, a rule, an equation

f(x) = 17 - x^2

now, for any value of x, we can determine the value of f(x)



let x=1

f(1) = 17-1^2


let x=5

f(5) = 17 - 5^2

Answer 35

f(1) - f(5) = (17-1)-(17-25) = -1+25