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Show that the curve $y=\sqrt{x^{2}+4 x}$ has two slant asymptotes: $y=x+2$ and $y=-x-2 .$ Use this fact to help sketch the curve.

There is no inflection point

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

06:52

Show that the curve $ y = …

04:11

Find the slant asymptote a…

02:47

07:14

Show that the lines $ y = …

02:34

Slant Aymptotes Find the s…

13:31

Find the slant asymptote, …

05:13

01:21

Determine all vertical and…

01:31

02:23

Graph functions that have …

01:39

02:10

07:37

Find the horizontal and ve…

00:57

Find an equation of the sl…

00:50

02:56

Sketch a graph of the rati…

08:20

04:45

02:53

04:30

Use the guidelines of this…

one main way that we could show that this graph has to slant. Assam totes would be, um, just by sketching the function. So we take y equals thes square root of X squared plus four x, Yeah, okay. And we'll remove this right here. We know that this graph, because the square root of something X squared that will it'll look somewhat like a absolute value function. However, it's slightly different. We have this curvature right here, a two beginning of the graph. But it's clear we will end up having to slant Assam totes because this line right here would be a slight Assam toe. And this line right here would be a slight Assam toe. Just because it's three square root of X squared plus four x, it becomes clear that as time goes on, one of the slain Assam totes will be X plus two. If you take the square root of that, it'll be something like X plus two eso We can graph that right here and then we would also have the equation of negative acts minus two. Okay, and this ties into the idea this relationship between square roots and squared and positive and negative, and all those come together to show us that these would both be slant Aston toads of the function.

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