Functions of two variables and partial derivatives, question 7

Topic: Functions of two variables and partial derivatives
Difficulty: Standard
Suggested time: 4 min
Marks: 3
Theory: UBC Math 100 §15.1Key results

A firm’s output is $Q(K, L) = 12K^{1/4}L^{3/4}$ units, where $K$ is units of capital and $L$ is units of labour. It now uses $K = 16$ and $L = 81$ . Which statement correctly gives and interprets the marginal product of labour, $\dfrac{\partial Q}{\partial L}$ , there?

With capital held at 16, one more unit of labour adds about 8 units of output.
With labour held at 81, one more unit of capital adds about 6 units of output.
With capital held at 16, one more unit of labour adds about 6 units of output.
With capital held at 16, one more unit of labour adds about 81/8 ≈ 10.1 units of output.
With capital held at 16, one more unit of labour adds about 129/8 ≈ 16.1 units of output.

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Theory UBC Math 100 §15.1Key results

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Functions of two variables and partial derivatives practice question 7