Problem 1. (1 point) Problem 4. (1 point) If 4x2 + 2x + xy =3 and y(3) = -13, find y'(3) by implicit differ- Find dy/ dx by implicit differentation: entiation. 2+7x = sin(xy) y (3) =. dy dx Problem 5. (1 point) Problem 2. (1 point) For the equation given below, evaluate y' at the point (-1, -2). Use implicit differentiation to find the slope of the tangent line to the curve defined by 2xy' + 7xy = 90 at the point (3,2). (3x - y) * + 2y' = -15. The slope of the tangent line to the curve at the given point is y' at (-1, -2) =. Problem 6. (1 point) Find the slope of the tangent line to the curve Problem 3. (1 point) Find y' by implicit differentiation. Match the equations defining y 4 sin(x) + 2cos(y) - 6sin(x) cos(y) + x =6x implicitly with the letters labeling the expressions for y'. at the point (61, 3n/2). 1. 3xsiny + 4sin2y = 2cosy Problem 7. (1 point) 2. 3xcosy + 4sin 2y = 2siny Find an equation of the tangent line to the curve 3. 3xcosy + 4cos2y = 2siny 2(x2 + 12) 2= 25(x2 - 2) 4. 3xsiny + 4cos2y = 2cosy 3 siny (a lemniscate) at the point (3, -1). A. y _3xcosy - 8cos2y - 2siny 3 cosy An equation of the tangent line to the lemniscate at the given B. y = 3xsiny - 8 cos 2y + 2cosy point is 3 sin y Problem 8. (1 point) C. y = gsin 2y- 3xcosy - 2 siny Let x3 + y3 = 28. Find y"(x) at the point (3, 1). 3 cosy D. y = 3xsiny + 8 sin 2y + 2cosy y(3) =