Question 1 If y is defined implicitly as a function of x by the equation 3x2 + 2xy + y2 = 6, find y' and y" when x = y = 1. Question 2 Find the slope of the curve xe") + 3x7 - 2y + 4 at the point (x, y) = (1,0). [Hint: The slope of the curve is y'(x)] Question 3 Prove that f(x) = x' + 4x + 2 has an inverse function g. With f(0) = 2, find g'(2). Question 4 Find the differentials: (a) d(x10 - 10) (b) d(In(x2+ 2) ) (c) d( VK + 1 /VR) Question 5 Let y be given implicitly as function of x by the equation xy + y' = 2x2. (a) Find y' and y" at the point (x, y) = (1, 1). (b) Find the quadratic approximation to y around x = 1, y = 1. [Hint: A quadratic approximation is Taylor's approximation of order 2.] Question 6 Find the elasticities of the functions given by the following formulas: (a) 10x-3 (b) 5xVx (c) 10+x (d) 2x + Inx