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Problem 33 Medium Difficulty

(a) The curve with equation $ y^2 = 5x^4 - x^2 $ is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1, 2).
(b) Illustrate part (a) by graphing the curve and the tangent line on a common screen. (If your graphing device will graph implicitly defined curves, then use that capability. If not. you can still graph this curve by graphing its upper and lower halves separately.)

Answer

a. $y=\frac{9}{2} x-\frac{5}{2}$
b.

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Video Transcript

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