Question

Let f(x) = 2-8/x+8/x^2. Find the open intervals on which f is increasing and decreasing. Then determine the x-coordinates of all relative maxima and minima

Answer 1

1st step find derivative

Answer 2

@myininaya okay so the derivative is (8/x^2)-(16/x^3), now what?

Answer 3

Combine the fractions and figure out when the f' is 0 or dne.

Answer 4

@myininaya I got x=2 and x=0

Answer 5

\[\frac{8x-16}{x^3}=0 => x=2 \]
Ok great!
Make a number line with 0 and 2 on it.
Then test the intervals around those numbers using f'
This will tell us if the function is decreasing or increasing on the intervals we test.

Answer 6

it is increasing from -infinity to 0, decreasing from 0 to 2, and increasing from 2 to infinity. how do i find the maximum and minimum values?