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Use the guidelines of this section to sketch the curve.$$y=\frac{x}{x^{2}+9}$$
$(0,3 \sqrt{3}),$ and $(-\infty,-3 \sqrt{3})$
Calculus 1 / AB
Chapter 4
APPLICATIONS OF DIFFERENTIATION
Section 4
Curve Sketching
Derivatives
Differentiation
Applications of the Derivative
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the following problem. We want to use the guidelines of the section to sketch the curve. Let's give me Y equals X over X squared plus nine. So we see the domain is a set of real numbers. Um The y intercept, If we plug in a zero will get zero so 00 point. And then we can also consider now the derivative of prime of X. And with a primer back screen of getting this is a Fedex. Mhm. We end up getting Crime affects, the function is going to be increasing until it reaches -3 or three. So here it's increasing but decreasing over those intervals. And then if we look at f double prime of X, we see that there's going to be an inflection point at X equals zero. So all these things considered, we end up looking here and we get that local minimum at negative three and the local maximum positive three with the inflection point at zero. So that's our final answer.
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