e :I.' Censidertneeuwe given by the implicit equation I + :.;.r2 = 1 tie 3 Find . t i :11: d3; d3 _ - - - 1 1 {in} Find an equation of the tangent line to curve at [3115151. y: Consider the curve given by the implicit equation x* + 3xy = 573 + 5 dy (a) Find dx dy dx (b) Find an equation of the tangent line to curve at (2, 1). V = ECeneider the curve given by the equation my; + my = It} Find an equation of the tangent line to curve at {5, 1}. y: Consider the curve given by the equation cy + 2x cos(y) = 2x (a) Find the slope of the tangent line to the curve at (4, IT). Answer: E (b) Find an equation of the tangent line to curve at (4, ). ESuppose that y2 + 9:1: 2 1:23; + 23, and y] = 5. {a} Find 2ft?) = I {h} Write the equation of the tangent line to the euwe y2 + Elm 2 may + 23 at the point {2, 5]. 1H= I Consider the curve given by the equation ~+ 4x + xy = 2 dy (a) Find dx dy (b) Use your answer from (a) and the equation of the curve to find as a function of c only. dy dx E day (c) Use your answer from (b) to find as a function of c only. dx2 E dax2Consider the curve given by the equation vity = 5 (@) Find the derivative y'. E (b) Use your answer from (a) and the equation of the curve to find y' (@). That is y' as a function of c only. y'(x) = E (c) Evaluate y' (9) = E (d) Use your answer from (b) to find y" (@) as a function of c only. y" (x) = EFind the slope of the tangent line to the curve 16(x2 + y?)2 = 200(x2 - y?) at the point (3, 1)