Question

Given the function f(x)=(x-2)/(x-5), determine an interval and a point when the average rate of change and instantaneous rate of change are equal

Answer 1

why? :)

Answer 2

ooh i can't read. determine an interval AND a point sorry

Answer 3

this is an open ended question. pick an interval, one that does not include 5 because the function is not defined there. pick any interval, but make it easy

Answer 4

ohh

Answer 5

so you want to pick or do you want me to pick?

Answer 6

u could pick it :) doesn't matter

Answer 7

it really doesn't matter, i would pick something simple, like say \([6,8]\)

Answer 8

we have some computation to do, namely
\[f(8)=\frac{8-2}{8-5}=\frac{6}{3}=2\] and
\[f(6)=\frac{6-2}{6-5}=\frac{4}{1}=4\] see, nice and easy

Answer 9

now we compute
\[\frac{f(8)-f(6)}{8-6}=\frac{2-4}{2}=-1\]

Answer 10

that is the average rate on that interval. last job is to take the derivative, set it equal to \(-1\) and solve for \(x\)
that is where the average rate of change will be equal to the instantaneous rate

Answer 11

but what is the derivative ? sorry i don't know it ?

Answer 12

derivative is
\[f'(x)=-\frac{3}{(x-5)^2}\] so your final job is to set
\[-\frac{3}{(x-5)^2}=-1\] and solve for \(x\) should be ok now right?

Answer 13

wait hold the phone.
if you do not know the derivative, then you cannot know the instantaneous rate of change. can't know what it means

Answer 14

i know the instantaneous rate of change :)

Answer 15

ok so you know the derivative, yes?

Answer 16

your final job in this one is to solve
\[-\frac{3}{(x-5)^2}=-1\]
\[-3=-(x-5)^2\]
\[(x-5)^2=3\]
\[x-5=\pm\sqrt{3}\]
\[x=5\pm\sqrt{3}\] the one that is in the interval \([6,8]\) is \(5+\sqrt{3}\)

Answer 17

wait ?

Answer 18

Do you know what a "derivative" is?

Answer 19

ok

Answer 20

never mind, i understand it :) thanks a lottttttttt (satellite73):)

Answer 21

yw

Answer 22

Nice job, @satellite73 , I don't know why you don't have a 100.

Answer 23

my score decrease, probably from every time i make a typo

Answer 24

hihi, u alway help me out :)

Answer 25

actually i don't know why
it was 100 and it went down. frankly i would perfer to remain undgraded

Answer 26

glad to help

Answer 27

Well, forgive me if I'm not that bothered by your 99. :P It's still an A+.