Part 1 - Algebra (1 point each) Solve each equation below for x. Show your work, and simplify your answers whenever possible. 1. 3x + 3 = 2(x + 14) 2. x - 9 = 6+4x 3. 6x _ 5-2(2+7) 4. x2 = 24 5. 3 ( 72 + 4x) = 15 6. 9x 2 = 1x2 7. 2x3 - 18 = -423 -16 Part 2 - Derivatives (1 point each) Take the derivative with respect to x for each of the functions below. 8. f(x) = 6x4 - 4x3 + 11x 9. f(2) = 322 - 323 -4 10. f(x) = 6x2 - 2x2 11. f(x) = 3In(x) - 3x3 12. f(x) = 1 In(4ac2) 13. f(x) = 5 In(4x - 4) Part 3 - Partial Derivatives (1 point each) 14. Compute ar of the function f(x, y) = 6xy3 + 2x2 - 3y3 15. Compute ay of the function f(x, y) = 6xy3 + 5x2 - 3y3 16. Compute ac of the function u(c, l) = ] In(c) + 3 In(1) 17. Compute g of the function u(c, l) = 4 In(c) + ? In(1) 18. Compute an of the function F(K, N) = 90K 3 N3 19. Compute an of the function F(K, N) = 90K3N3