In this lesson we are going to expand upon our knowledge of derivatives, Extrema, and Optimization by looking at Applications of Differentiation involving Business and Economics, or Applications for Business Calculus.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
We will begin by learning some very important business terms and formulas, such as:
- Cost Function
- Total Revenue
- Average Cost
- Profit Function
- Marginals
- Demand Function
We will quickly see that all of these applications questions are exactly like the Optimization questions we learned earlier.
In fact, they also closely mimic how we find Absolute Extrema! Take a derivative and set it equal to zero!
Simple!
But, if you’re anything like me, then the hardest part about any of these problems is coming up with the right formula.
Marginal Cost and Revenue Formulas
Don’t worry, I’m going to show you how a surefire method for how to come up with the right formula every time, and use it appropriately for these optimization applications problems.
Here’s a big hint…
…the key is being able to write the equation of a line!
Together we will look at 9 questions in detail, where we will be maximizing or minimizing such things as Revenue, Profit, Average Cost, Marginals, etc., by using all of our skills of the First and Second Derivative Tests.
And as Paul’s Online Notes nicely states, with this lesson we will hopefully begin to appreciate Calculus is far reaching, cross-curricular, and used in other fields.
Demand Function – Video
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