# How do you determine whether the function #f(x)= -6 sqrt (x)# is concave up or concave down and its intervals?

##### 1 Answer

Use calculus (the sign of the second derivative) or algebra/precalculus graphing techniques.

#### Explanation:

**Calculus**

In general, to investigate concavity of the graph of function

Note first that the doamin of

The graph of

(Intervals of concavity are generally given as open intervals.)

**Algebra/Precalculus**

The graph of the square root function looks like this:

graph{y = sqrtx [-10, 10, -5, 5]}

That graph is concave down.

Multiplying by

graph{y = -6sqrtx [-6.41, 25.63, -13.2, 2.82]}

The graph is concave up.