1. Given 2x²y - 2y³ = 3x + 7 , use implicit differentiation to find the derivative y'=dy/dx and then find the equation of the tangent line to the given curve at the point (x,y)=(3,1).

2.If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 62 -x/12. How many candy bars must be sold to maximize revenue?

3. Sketch the graph of a continuous function f on the given domain that satisfies all conditions. f has domain [-4, 4]; f(-4) = 0; f(4) = 4; f'(x) < 0 on (-2, 2); f'(x) > 0 on (-4, -2) (2, 4) f''(x) < 0 on (-4, 0); f''(x) > 0 on (0, 4)

4. Graph the equation. Include the coordinates of any local and absolute extreme points and inflection points. y = 18x/x^2+9

5.Find two numbers such that their difference is 12and their product is minimal.Write down your complete solution,including all steps as well as a clear statement of your final answer.You may use the math editor, or, if you prefer, plain text, for example using x^2 (for the square of x), x(x+5)=0 (for a sample equation), and x/(x-3) (for division).