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Functions : First and Second Derivatives, Asymptotes and Intervals of Increase - y=(x+1)/(x^2-4)

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?

Solution Preview

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 ...

Solution Summary

First and Second Derivatives, Asymptotes and Intervals of Increase are investigated.

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