Active Calculus - Gvsu - Grand Valley State University

2.7. DERIVATIVES OF FUNCTIONS GIVEN IMPLICITLY 59Activity 2.20.Consider the curve defined by the equation y(y 2 − 1)(y − 2) = x(x − 1)(x − 2), whose graph ispictured in Figure 2.5. Through implicit differentiation, it can be shown that2y11 2 3x-1Figure 2.5: The curve y(y 2 − 1)(y − 2) = x(x − 1)(x − 2).dy (x − 1)(x − 2) + x(x − 2) + x(x − 1)=dx (y 2 − 1)(y − 2) + 2y 2 (y − 2) + y(y 2 − 1) .Use this fact to answer each of the following questions.(a) Determine all points (x, y) at which the tangent line to the curve is horizontal.(b) Determine all points (x, y) at which the tangent line is vertical.(c) Find the equation of the tangent line to the curve at one of the points where x = 1.⊳