Ap Calculus, Intervals

Question

Determine the open intervals whewhere the graph of f (x)=-(1)/(x+1)^2 is concave up or concave down.

Answer 1

Second derivative of the function is f"(x)=-6(x+1)^-4 ,which is negative on both (-inf,-1)and(-1,inf),
So the function is concave down on each of intervals.

 

Answer 2

f(x) = -1/(x + 1)²

For all values of x, f(x) < 0.

A vertical asymptote is at x = -1.

On the left side of x = -1, the graph is concave to the left.

On the right side of x = -1, the graph is concave to the right.