Im having a problem with curve sketching i cant figure out how to do this problem. I am confused. Heres the question 1. For the following curve find: a)the domain b)the intercepts c)the asymptotes d)intervals of increase or decrease: local maximum and minimum e)concavity and the point of inflection x^2 - x - 1 / x-1 Heres my work. a) the domain is x = 1 b)Let y=0 y = 0 - 0 - 1/ 0-1 y=1 Let x = 0 x^2 - x - 1 = 0 x = 1.62 or x = 0.62 c) Vertical asymptote: x = 1 Horizontal asymptote x^2 - x - 1 / x-1 y = x - 1/ x-1 Therefore it has an slant asympote at y = x Heres where it gets fun d) y = x^2 - x - 1/x-1 y'= x^2 - 2x + 2/ (x-1)^2 let y'= 0 x^2 - 2x - 2 = 0 x = 1 +/- i Do i say that it doesnt have an maximum or minimum point because they are imaginary? e) y'' = -2/(x-1)^3 Let y''=0 -2 cannot equal 0 So there are no points of inflection, but then how do i determine the concavity when my first derivative is based on imaginary numbers. I have never encountered one like this. I dont know how to determine the intervals of decrease or increase because of i, so can you please help me.