# Curves and Implicit Diﬀerentiation

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1 Lemniscate of Bernoulli The lemniscate of Bernoulli is a curve deﬁned by the equation (x 2+y 2) = x2 −y . (1) The graph of this curve is a ﬁgure eight (Figure 1).-1-1 €€€€ 2 1 €€€€ 2 1 Figure 1: Lemniscate of Bernoulli Suppose that we wish to ﬁnd the x-coordinates of points on the curve that have a horizontal tangent line.

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1 Lemniscate of Bernoulli The lemniscate of Bernoulli is a curve deﬁned by the equation (x 2+y 2) = x2 −y . (1) The graph of this curve is a ﬁgure eight (Figure 1).-1-1 €€€€ 2 1 €€€€ 2 1 Figure 1: Lemniscate of Bernoulli Suppose that we wish to ﬁnd the x-coordinates of points on the curve that have a horizontal tangent line.
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©a Q2V0q1F3 G pK Huut Pal 6Svorf At8w 3a 9rne f kL jL tC 4.M d mAQlyl 0 9rMiAgJhyt vs0 Rr9e ZsKePr Evje edm.M s QMdawd3e7 DwciJt VhU WIbn XfJiQnLivtSe3 1C4a 3l bc Vuol4uWsr. 2 Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Implicit Differentiation Date_____ Period____
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©a Q2V0q1F3 G pK Huut Pal 6Svorf At8w 3a 9rne f kL jL tC 4.M d mAQlyl 0 9rMiAgJhyt vs0 Rr9e ZsKePr Evje edm.M s QMdawd3e7 DwciJt VhU WIbn XfJiQnLivtSe3 1C4a 3l bc Vuol4uWsr. 2 Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Implicit Differentiation Date_____ Period____
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