Q.Given the Total Cost function, TC=15+3Q+7Q² derive the marginal cost function.

Marginal cost is the derivative of total cost with respect to output. Differentiating TC = 15 + 3Q + 7Q² gives MC = 3 + 14Q.

Marginal Cost (MC) is the addition to total cost from producing one more unit of output. When TC is given as a continuous function of output Q, MC is the first derivative of TC with respect to Q:

MC = dTC / dQ

Given: TC = 15 + 3Q + 7Q²

Differentiate term by term:

• derivative of 15 (a constant, the total fixed cost) = 0
• derivative of 3Q = 3
• derivative of 7Q² = 14Q

Therefore: MC = 0 + 3 + 14Q = 3 + 14Q

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