In: Math
1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values?
2. What are inflection points? How do you find them?
3. What does the sign of the derivative, f ', tell us about the function? What does the sign of the 2nd derivative, f ", tell us about the function?
4. What does it mean to say that a function is concave upward? Concave downward?
5. What does the Extreme Value Theorem say? Explain how to find the absolute extrema of a continuous function on a closed interval.
6. Explain how to use the 2nd derivative to find the relative maxima and relative minima of a function.
7. What is the meaning of Δy/Δx? What is its geometric interpretation? What is the meaning of dy/dx? What is its geometric interpretation?
8. For which functions is dy/dx equal to Δy/Δx?
9. When is dy about equal to Δy?
10. What is marginal cost? If C(x) is a cost function, how would we find the marginal cost when x = 50? What does it represent?