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Problem 43 Hard Difficulty

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

Answer

$$\left(\pm \frac{5 \sqrt{3}}{4}, \pm \frac{5}{4}\right)$$

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Video Transcript

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.