Question

let f(x)=1/x.find a number b so that the avg rate of change of f(x) on the interval [-b,b] is the value 1/2...how do i even set this up??

Answer 1

\[ARC = \frac{f(x_2)-f(x_1)}{x_2-x_1}\]
\[= \frac{f(b)-f(-b)}{b-(-b)}\]
\[= \frac{\frac{1}{b}-\frac{1}{-b}}{b+b}\]
\[= \frac{\frac{1}{b}+\frac{1}{b}}{2b}\]
\[= \frac{\frac{2}{b}}{2b}\]
\[=\frac{2}{b} \cdot \frac{1}{2b}\]
\[=\frac{1}{b^2}\]
We need the above fraction to be 1/2 so that means b^2 = 2, or b = sqrt(2).

Answer 2

wouldn't it be 2b times 2 not 2 times 1on ur 2nd 2 last step? (dont u have to flip the fraction when u go from divide to mult.?

Answer 3

i believe that is the step im confused on..

Answer 4

ohhh, nvm got it.

Answer 5

cool...