Consider the function g(x)=(x^4+1)/(x^3+x^2) (a) find its horizontal, vertical, and slant asymptotes, if it has any. (b) we have computed the first derivative, and we found that the only values of x for which g '(x)=0 are x=-2.2, x=-0.6, x=1.15. Also g'(1000)0 and g'(-1000)0 and g'(-1000)

Question

Consider the function g(x)=(x^4+1)/(x^3+x^2) (a) find its horizontal, vertical, and slant asymptotes, if it has any. (b) we have computed the first derivative, and we found that the only values of x for which g '(x)=0 are x=-2.2, x=-0.6, x=1.15. Also g'(1000)>0 and g'(-1000)<0 . Use this information, your knowledge of the asymptotes from the previous question, and whatever else you need to sketch the graph of g. For this particular question, you do not have to look at concavity. Consider the function g(x)=(x^4+1)/(x^3+x^2) (a) find its horizontal, vertical, and slant asymptotes, if it has any. (b) we have computed the first derivative, and we found that the only values of x for which g '(x)=0 are x=-2.2, x=-0.6, x=1.15. Also g'(1000)>0 and g'(-1000)<0 . Use this information, your knowledge of the asymptotes from the previous question, and whatever else you need to sketch the graph of g. For this particular question, you do not have to look at concavity. @Mathematics

alfie · Answer

Study the function, find the points where it is not defined and to the limit for x->point of the function.

limx->+infinity of the function for horizontal.

Use the formula of the vertical ones to find it.

anonymous · Answer

Is it vertical asymptotes x=0 and x=-1? Also i got y=x for slant asymptote. And no horizontal asymptote. Is that correct?

alfie · Answer

Verticals are correct, so it is horizontal. The slant one I am too lazy too apply the formula :)

anonymous · Answer

okay.