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6. Consider the curve given by the equation 2(x - y) = 3 + cos y. For all points on the curve, dy <

6. Consider the curve given by the equation 2(x - y) = 3 + cosy. For all points on the curve, jis reino < 2. (a) Show that =

(b) For - <y< , there is a point Pon the curve through which the line tangent to the curve has slope 1. Find the coordinates

(c) Determine the concavity of the curve at points for which - <y< . Give a reason for your answer.

(d) Let y = f(x) be a function, defined implicitly by 2(x ? y) = 3 + cos y , that is continuous on the closed interval 2, 2.1

6. Consider the curve given by the equation 2(x - y) = 3 + cos y. For all points on the curve, dy < 2. da 2/3 (a) Show that = dy dr 2 2-sin y (b) For - (c) Determine the concavity of the curve at points for which - (d) Let y = f(x) be a function, defined implicitly by 2(x - y) = 3 + cos y, that is continuous on the closed interval [2, 2.1] and differentiable on the open interval (2, 2.1). Use the Mean Value Theorem on the interval [2, 2.1] to show that (2.1) (2) . 15

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