How do you graph #y=(x^3-8)/(6-x^2)# using asymptotes, intercepts, end behavior?
1 Answer
Dec 21, 2016
Slant asymptote:
Explanation:
By actual division.
horizontal asymptote y = quotient = -x and vertical asymptotes
The y-intercept is -4/3 and x-intercept is 2.
y' is 0 at
Local maximum ( for y'' < 0 ) at x = 3sqrt2, local minimum ( for y''>0 )
at x = -3sqrt2 and point of inflexion ( for y'' = 0 and y''' not 0 ) at x = 0.
Look at the graph that illustrates all these aspects.
graph{y(6-x^2)-x^3+8 =0 [-38.28, 38.28, -19.14, 19.14]}