# Is #f(x) =sqrt((x-12)(-x+3))-x^2# concave or convex at #x=6#?

##### 1 Answer

Convex.

#### Explanation:

To know if a function is concave or convex you use the second derivative and you substitute

Let's derivate one time,

and now let's derivate again,

it only remains substituting,

and so the number we get is negative, it means that the funcion is convex, as we can see in the graph below:

graph{sqrt((x-12)(3-x))-x^2 [-3.25, 42.34, -21.04, 1.77]}