The meaning of derivative and its units.
The function is the cost of production.
The cost of production is depends on number of ounces of gold produced.
That is, the cost of production is a function of ounces of gold produced.
Note that, the derivative is the instantaneous rate of change of C with respect to x,
The derivative is rate of change of the production cost with respect to the number of ounces of gold produced.
The instantaneous rate of change is equal to .
Here is measured in dollars and is measured in ounces.
Thus, the units are dollars per ounces.
The meaning of .
After 800 ounces of gold produced.
The rate at which the production cost is increasing is 17 dollar per ounce.
The cost of producing the 800th ounce is about 17 dollar.
That is, when , the production cost is increasing 17 times as fast as number of ounces of gold produced.
To check: Whether the derivative will increase or decrease for short term and also for long term.
In the short term,
The rate of production cost decreases as the production cost involves more the startup cost for the mass production. Hence, the values of will decrease as x increases.
But, the derivative might increase due to large-scale operations.
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