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OpenStudy (anonymous):
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
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myininaya (myininaya):
1st step find derivative
OpenStudy (anonymous):
@myininaya okay so the derivative is (8/x^2)-(16/x^3), now what?
myininaya (myininaya):
Combine the fractions and figure out when the f' is 0 or dne.
OpenStudy (anonymous):
@myininaya I got x=2 and x=0
myininaya (myininaya):
\[\frac{8x-16}{x^3}=0 => x=2 \] 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.
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OpenStudy (anonymous):
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?
OpenStudy (loser66):
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