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Use the guidelines of this section to sketch the curve.$$y=\frac{x^{2}}{x^{2}+9}$$

$\left(-\sqrt{3}, \frac{1}{4}\right)$ and $\left(\sqrt{3}, \frac{1}{4}\right)$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

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In mathematics, precalculu…

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In mathematics, a function…

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Use the guidelines of this…

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the following problem. We're gonna be considering the function X squared over X squared plus nine. Let's see. The domain is all real numbers. So there's not going to be um vertical awesome tote but there will be a horizontal assam tote. Why it was one. There's also going to be um an intercept of 00. Also um We see that bye. Considering um the derivative of the graph. We see that there is going to be a local minimum at 00. And then looking at the 2nd derivative graph, we see that there's gonna be two inflection points here and here. So we expect to see kind of a bell shaped curve that's upside down based on the given information. So graphing our function, we see in fact this is the somewhat of a battle shaped curve upside down but more spread out has the correct local minimum as well as the inflection points where we expected them to be. So that's our final answer.

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