In problem #14, find the Derivative of each expression. Use correct notation for each Derivative! NOTE: Algebraic simplification of each Derivative result is NOT required. Then do each part of problem #5, an application of derivatives for Marginal Analysis.

1) y = (3x^1.5 - 1.5x² ) ( 12x³ + 135)

2) y = (6t⁴ - 3t^2.5 + 800) (t^3.5 + 25t^-2)

3) f (t) = 11t³ - 8t^1.5 /4t^2.2 + 13

4) f(x) = 41x^0.7 - 100x^1.4 / 3600 + 8x^2.5

^{Answer all parts of Problem #5 below. Show all work! (Refer to Module #4 for Examples and terminology.) 5) A local company makes and sells cabinet hinges for modular homes. Selling price "p" per hinge is related to weekly demand "X" by the relation: p = 12 - 0.002x ("p" measured in dollars). The company's total cost per week is given by: C(x) = 4.25X + 3250}

^{a) Find the expression for the company's Revenue function.}

^{b) Find the expression for the company's Marginal Revenue.}

^{c) Find the Incremental Revenue associated with the 1801st hinge that is made and sold in a week. (Solve to the nearest penny.)}

^{d) Find the expression for the company's Profit function.}

^{e) Find the expression for the company's Marginal Profit.}

^{f) Find the Incremental Profit associated with the 1000th hinge that is made and sold in a week. (Solve to the nearest penny)}