Points of inflection of f(x) = (x + 3) / (x + 2)

[cmnalo]

If f(x) = (x + 3) / (x + 2) is concave downward on the interval (infinity, -2) and concave upward on the interval (-2, infinity), how do you find any points of inflection, if any?

Answer: There are none.

 

[skeeter]

yes ... there are no points of inflection on the curve.

the second derivative changes sign at x = -2 ... but, the function is not defined at x = -2.

 

[galactus]

There is a vertical asymptote at x=-2. The curve is undefined there.

To find inflection pts, you can set your f''(x)=0 and solve for x(assuming there is concavity change).

In this case, \(\displaystyle f''(x)=\frac{2}{(x+2)^{3}}\)

As you can see, it is undefined at x=-2

There are no inflection points.

Edit[tkhunny]: I'm SURE you meant "vertical".