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Solve the given problems by using implicit differentiation.At what point(s) does the graph of $x^{2}+y^{2}=4 x$ have a horizontal tangent?

Calculus 1 / AB

Chapter 23

The Derivative

Section 8

Differentiation of Implicit Functions

Derivatives

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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Horizontal Tangent At what…

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04:35

At what points do the grap…

question. They give us the following function, and they want us to determine when the horizontal lines are the tender lines of horizontal. So let's take our rooted because, like this slope for excuse minus four X and mom is this is a slope. When it's equal to zero, we confined our relevant, um, points where the slope zero for the X cordant on weaken plot in X actually. And then let's pull out an X squared minus one. Let's see you expand this. You'll get the above. So actually at X equals zero minus one and plus one will have or is on the line blood seeing. And so what does that mean? Muncie, This is a X to the Boris function. So it's gonna go to positive infinity from both actions. Probably gonna look something lying. But in this will you ever get negative? We put in a one everywhere zero everywhere. No. Well, it could be shifted, but it probably looks something like this. You get let's say this is no, actually and yeah, but let's say this is negative. One might say this is positively and thats zero well, our attention lines horizontal, that negative one So it looks like this. Something that one looks like this. And ah, zero. It looks like this. What we noticed around this points law, this is the lowest point from all the points nearby on the graph. Most value of why something here and here. It's the highest value of why, for all nearby small areas, cool.

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