Please show work 1) Use implicit differentiation to obtain dy/dx in terms of x a

ID: 3341459 • Letter: P

Question

Please show work

1) Use implicit differentiation to obtain dy/dx in terms of x and y for the following equation: (x^2 + y^2)^2 = 4x^2y

2) What is f'''(x) given f(x)= (x^5 -3x^4 + 4x^2 -2x +1) / x^2

3) Find f ' (x) and determine when f ' (x) = 0 in the interval [0, 2pi] given that f(x) = sinx + (cos^2 x) / 2

4) The surface area of a right circular cylinder is given by S= 2pir^2 + 2pirh

a) Find the rate of change of the surface area, S, with respect to the radius, r, given height, h, is constant.

b) Find the rate of change of the height, h, with respect to the surface area, S, given the radius. r, is constant