Asked by Andreia
discuss the curves under the headings given in this section
y=x/x-1
y=x/x-1
Answers
Answered by
Steve
I assume you mean asymptotes, max/min, etc.
y = x/(x-1)
y' = -1/(x-1)^2
y'' = 2/(x-1)^3
hor. asymptote at y=1 since degree is the same top and bottom. As x gets large, y acts like x/x = 1
vertical asymptotes where denominator is zero
max/min where y' = 0 and y'' not zero
increasing where y' > 0
concave up where y'' > 0
inflections at y'' = 0
Take it awaaaay!
y = x/(x-1)
y' = -1/(x-1)^2
y'' = 2/(x-1)^3
hor. asymptote at y=1 since degree is the same top and bottom. As x gets large, y acts like x/x = 1
vertical asymptotes where denominator is zero
max/min where y' = 0 and y'' not zero
increasing where y' > 0
concave up where y'' > 0
inflections at y'' = 0
Take it awaaaay!
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