Question

let F(x)=1/t for t>0
Find the average rate of change of f over the interval (2,3) then repeat for the interval (2,T), where 2 11 years ago

Answer 1

Hey there,
\(\Large\rm f(t)=\dfrac{1}{t}\)

Average rate of change from 2 to 3:
\(\Large\rm \dfrac{f(3)-f(2)}{3-2}\)

Answer 2

\(\Large\rm f(\color{royalblue}{t})=\dfrac{1}{\color{royalblue}{t}}\)

\(\Large\rm f(\color{royalblue}{3})=\dfrac{1}{\color{royalblue}{3}}\)

Answer 3

What'dyou think jp? :O
Confusing stuff?

Answer 4

the first part isnt too confusing then second part is mostly where im struggling with

Answer 5

and thanks for the help

Answer 6

Remember your slope formula? (y2-y1)/(x2-x1)
This is the same idea, but now you're using function notation instead of y's.

\(\Large\rm \dfrac{f(3)-f(2)}{3-2}=\dfrac{\frac{1}{3}-f(2)}{3-2}\)

So we're evaluating the function at t=3,
That's what f(3) is.

And then we're plugging that value into our slope formula.
How bout f(2)?
What do you get when you plug 2 in for your t? (from the original function).

Answer 7

if i plugged in 2 for my t ill get 1/2, so you saying after i get answer i have to put it into the slope formula?

Answer 8

Mmmm, good. Yes. Plug it in.
\(\Large\rm \dfrac{\frac{1}{3}-\frac{1}{2}}{3-2}\)

Do you understand how to simplify this?

Answer 9

find a common denominator so -1/6 divided by 1