Problem+51+Sharon+O+and+Anders

//f(x) = e⌃-1/(x+1) f'(x) =// //e⌃-1/(x+1) · 1/(x+1)^//2 f''(x) =(//(e⌃-1/(x+1) · 1/(x+1)^//2) //·// //1/(x+1)^//2)+ (-2(x+1)/(x+1)^4)(//e⌃-1/(x+1))//

//a) Find all vertical and horizontal asymptotes.

you have the function e^-1(x+1) to find the vertical asymptotes you must find values of x that cannot exist, in this problem there is a fraction which makes the vertical asymptote easy to find, simply take the fraction -1/(x+1), and find what value of x will make the denominator 0, which will create a vertical asymptote, x+1=0 x=-1 so you know there is a vertical asymptote at x+-1.

Horizontal asymptote at y= 1 b) increasing// //(-//∞//,-1),// //(-1,//∞) //c) No max. or min. d) concave up (-//∞//,-1), (-1,-1/2) concave down (-1/2,//∞) inflection point (-1/2, 1/e^2) e) GRAPH