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]}