A few days ago
Mark M

asymptote, concave regions, inflection point #2?

f(x)= x^3/(x^2-4)

defined on the interval [-15,15]

vertical asymptotes??

concave up on the region ? to ? and ? to ?

inflection point?

Top 1 Answers
A few days ago
Anonymous

Favorite Answer

Vertical asymptotes:

x = -2 and x = 2

To find concavity regions and inflection points, find the second derivative and check its sign:

f’ = (x^4 – 12x^2)/(x^2 – 4)^2

f” = 8x(x^2 + 12)/(x^2 – 4)^3

The curve is concave up <=> f” > 0 or on the intervals (-2, 0) and (2, +infty).

It is concave down on (-infty, -2) and (0, 2).

Iflection points: x=-2, x=0, and x=2.

You can email me if you want more detailed solution.

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