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Find the points on the lemniscate in Exercise 31 where the tangent is horizontal.

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00:57

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Campbell University

Oregon State University

Baylor University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

08:55

Find the points on the lem…

18:36

05:01

Find the points on the gra…

02:21

Find the points with a ho…

02:14

Horizontal Tangent Line In…

01:58

Find all points on the gra…

00:29

Horizontal and Vertical Ta…

01:16

Find the points on the cur…

in this problem where us to use the question given in exercise regularly and west find the ordinance off the present attention. So basically, we first need to the French Air Destructor X. Let's do that. We have four times. Expert Buzz Weisberg, Times David Talked Inter function, which is to eggs waas to our times y prime physical to 25 times two X minus two. Why crime? All right, we know that, uh, tension lines were gentle. One before Stuart zero. So let's set what 00.0 we have, then four times. Expect for spirit Times two X is equal to 25 times two x From this, we got any questions off a form to x times four times x great plus y squared minus 25. Physical zero. Now we want this to hold. It means that this should be zero. So this will give us a relationship between exit. Why we have ex scraped bus. Weisberg is equal to 25 or four. Now let's say that this is our question them to end. The orginal main question is a question or, um, because you could use any old one punch and silver using want and to so using one and two. We see that Why could be positive. Negative plus minus four. Why is this? We can use question number. Judy Clark X. We have Expert is equal to 25 44 minus y spirit. So the name described is 25 4 uh, minus 25 for 16 that iss 75 over 16. So this means that X could be plus by this five scourge on +34 Combining these two, we find accordance as post minus fire. Um, Skurdal three over four plus minus five over four.

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