A firm has the Cobb-Douglas production function y = 10x}^^x!7²x}^. Currently, it is using the input bundle (27, 16, 64). a) How much is it producing? b) Use differentials to approximate its new output when x increases to 27.1, x2 decreases to 15.7, and x, remains the same. c) Use a calculator to compare you answer in part b with the actual output.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.