# How do you find intercepts, extrema, points of inflections, asymptotes and graph #h(x)=xsqrt(9-x^2)#?

##### 1 Answer

Please see below.

#### Explanation:

**Domain** :

**Intercepts**

(Solve

**Asymptotes**

The function has no horizontal asymptotes. (The domain is bouinded.) and no vertical asymptotes (there is no division).

Is undefined only at the endpoints of the domain and is

It is worth noting that as

**Local extrema** and increasing/decreasing

On

On

And

#h(-3/sqrt2) = -9/2# is a local minimum.

On

On

And

#h(3/sqrt2) = 9/2# is a local maximum.

**Concavity** and inflection points

Is undefined only at the endpoints of the domain and is

On

On

The point

The graph is:

graph{xsqrt(9-x^2) [-9.23, 13.27, -5.625, 5.625]}