Question

for the curve y=(x^2+1)/(x^2-4), find:
(i). The cordinates of the turning points
(ii). The equations of the asymptotes
(iii). Sketch the curve

Answer 1

dy/dx = (2x(x^2 -4) - 2x(x^2+1))/(x^2-4)^2
= (2x^3 - 8x - 2x^3 - 2x)/(x^2-4)^2
= -6x/(x^2-4)^2
= 0 for max/min or turning points

6x/(x^2-4)^2 = 0 ---> x = 0
then y = -1/4
the turning point is (0, -1/4)

asymtotes .... when the denominator is zero
x^2 - 4 = 0
x = ± 2

VA at x = 2 and x = -2

http://www.wolframalpha.com/input/?i=plot+y%3D%28x%5E2%2B1%29%2F%28x%5E2-4%29