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# (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.

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

in this problem. We're going equation and impart there. Where else? To cross this question. You could use any online function, porter or even your calculators if you graph it. This is what a bunch of looks like. And it is a case in part, you left by words and the patient. So basically being to purse appreciate this equation with respect, Ex Lester that we have six. Why square times y prime plus two y four prime finest five party support. Why? Prime is equal to four excuse, but six x grade waas to ex promise. We see that then why Prime is equal to four excuse by six Expert off to X You wanted by six Weisberg plus two y minus five y to the fourth for essential tensions are pouring for the percentage is zero. So we're gonna set Why prime to be easier? It means that Liberator should be zero or excuse by the six x squared plus two x should be zero that is two x times two X minus one times x one staunch zero. So from this we see that X coordinates A portent of paintings are at X zero Excellent health. The next one

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp