If the total cost function is C(x) = 0.5x² + 20x + 100, find the marginal cost when x = 10.

The total cost of producing x units is C(x) = 2x² + 10x + 50 and the revenue is R(x) = 40x. Find the level of output at which the profit is greatest.

The demand function is x = 100 − 2p. Find the elasticity of demand when p = 20.

If the demand function is p = 50 − 2x, find the marginal revenue when x = 5.

Define the break-even point and the elasticity of demand.

If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.

Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.