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How to Find Cost-minimizing Input with GeoGebra

Use GeoGebra to find the optimum level of production that minimizes the production costs of a business.

GeoGebra Instruction 1

1.: Open Algebra View and Graphics View under View in Menu.
2.: Enter the cost function in Algebra View by typing C = <cost function> and pressing Enter.
3.: Enter the unit cost function in Algebra View by typing U = Expand(C/x) and pressing Enter.
4.: Enter C’ in Algebra View and press Enter.
5.: To view only $C^{'} (x)$ and $U (x)$ in Graphics View, tap the dot in front of $C (x)$ . The graph of $C (x)$ is hidden when it is unchecked.
6.: In order to find the points of intersection between $U (x)$ and $C^{'} (x)$ , press Intersect in Toolbar and then click on the graphs of $U (x)$ and $C^{'} (x)$ .
7.: The $x$ -coordinate of the intersection point $A$ is the cost-optimal production level.

Screenshot of GeoGebra showing the intersection of U(x) and C’(x)

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