Functions : First and Second Derivatives, Asymptotes and Intervals of Increase - y=(x+1)/(x^2-4)
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Y=(x+1)/(x^2-4)
1) Find dy/dx and second derivative
2) What are the asymptotes?
3) Intervals of increase? intervals of upward concavity? Points where the horizontal line is tangent?
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Solution Summary
First and Second Derivatives, Asymptotes and Intervals of Increase are investigated.
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denominator x^2 - 4 = (x - 2)(x + 2) s o the vertical asymptotes are at x = 2, x = -2.
there's a horizontal asymptote : y = 0 (gotten by taking the limit lim f(x) as x -> oo.
dy = [ (x^2 - 4)(1) - (x+ 1)(2x)]// [x^2 - 4]^2
dx
simplifying the numerator : x^2 - 4 - 2x^2 - 2x = - x^2 - 2x - 4 = - (x^2 + 2x + 4) = 0
has no ...
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