Problem

Find the points on the lemniscate in Exercise 31 …

02:18

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Problem 42 Medium Difficulty

(a) The curve with equation
$ 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 $
has been likened to a bouncing wagon. Use a computer algebra system to graph this curve and discover why.
(b) At how many points does this curve have horizontal tangent lines? Find the $ x- $ coordinates of these points.

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Video Transcript

In this problem were given an equation and in part they were as to graph this equation, you could use any 1 function potter or even your calculators if you grab it. This is what the function looks like that is behaves in part. We were asked to find horizontal tensions, so basically we need to first differentiate this equation with respect to x, less to that we have 6 y squared times y prime plus 2 y times y prime minus 5 y to the prime is equal to 4 x. Cube minus 6 x, squared plus 2 x from this we see that then y prime is equal to 4 x cubed minus 6 x square of 2 x, divided by 6 y square plus 2 y minus 5 y poseur. Horizontal engines are pouring a 0, so we're going to say y prime to be 0. It means that numerator should be 0, so 4 x, cubed, minus 6 x, squared plus 2 x, should be 0, that is 2 x times 2 x, minus 1 times x. Minus 1 should be 0, so from this we see that x, coordinates of horizontal tangent are t x, 0, x, 1, half and x, 1.

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Problem

Find the points on the lemniscate in Exercise 31 …

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Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Catherine Ross

Anna Marie Vagnozzi

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Grace He

Catherine Ross

Anna Marie Vagnozzi

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Catherine Ross

Anna Marie Vagnozzi

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals