Max and Min
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Lesson Description:
Understand how the derivative of a function can be used to identify inputs that may correspond to extrema (maxima or minima) of the function. Be able to find the actual extrema of a function. Note: using technology may be the easiest way.
Check out www.themathdude.org for more videos.
Additional Resources:
- Definition of marginal cost - Definitions of such words as marginal benefit, marginal cost, and marginal profit
- Marginal Cost Explanation - An explanation of maximizing profit using the Marginal cost-marginal revenue method -- look about halfway down the page for the explanation.
- Average Cost Explanation - An explanation of average cost with formula included
- Marginal Cost Explanation - An explanation of marginal cost and what it means including formulas
- Maximize Revenue Notes - Notes on how to maximize revenue
Questions answered by this video:
- How can you find the maximum or minimum values of a function?
- How can you find the max or min values of a function by using the MAX and MIN functions on a TI graphing calculator?
- How can you find the max or min values of a function by using the table on a TI graphing calculator?
- How can you use the ZERO feature and the Equation Solver on the TI graphing calculator to find where the derivative of a function is equal to 0?
- How does the derivative of a function tell you where the function has a maximum or minimum?
- How can you find where a function has a max / min by finding where the derivative equal 0 by hand?
- How can you find the value of the max / min for a function using the derivative function?
- Why is the vertex of a quadratic function x = -b/2a?
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Staff Review
This lesson explains how to find the maximum and minimum values of a function. A TI graphing calculator is used in some of the methods for finding max and min. The graph and table features are used to find the max / min of the function. Then, the zero function and the equation solver is used to find where the derivative of the function is zero. Finally, you will see how to find the derivative and solve by hand.
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