# For what values of x is #f(x)=(-2x)/(x-1)# concave or convex?

##### 1 Answer

Study the sign of the 2nd derivative.

For

For

#### Explanation:

You need to study curvature by finding the 2nd derivative.

The 1st derivative:

The 2nd derivative:

Now the sign of

For

For

**Note**: the point

Here is a graph so you can see with your eyes:

graph{(-2x)/(x-1) [-14.08, 17.95, -7.36, 8.66]}