1. P1: Economic Applications of Functions and Derivativesa. Sketch the graph of the short run total cost function TC = 3q² +5g +300, forq=0 to q = 15;b.Find the marginal and average cost functions. Sketch their graphs.c. Explain in words why average cost is greater than marginal cost at all levels ofoutput;d. How does the difference between marginal and average cost, MC – AC,behave as 9 increases without limit?2. P2: Economic Applications of Functions and Derivativesa. A firm's short run total cost function is TC = 0.5q² +q+500. The firm sells ina perfectly competitive market and the ruling price is P = 61b. Find the most profitable level of output, and the profits at that output.c. Sketch the graphs of total cost and total revenue with the same axes, and do thesame with marginal cost and marginal revenue. Sketch the graph of the profitfunction. Indicate in all diagrams the equilibrium values of the variables.3. P3: Elasticitya. Using the demand function: Q = -3p²+2p+ 1965. Find the total revenueand marginal revenue functions (as functions of q).b. Find the point elasticity (1) when P = 10; (2) when P = 24.c. Sketch the demand function.

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1. P1: Economic Applications of Functions and Derivatives a. Sketch the graph of the short run total cost function TC = 3q² +5g +300, for q=0 to 9 = 15; b. Find the marginal and average cost functions. Sketch their graphs. c. Explain in words why average cost is greater than marginal cost at all levels of output;