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In: Math

1. What is a critical number of a function f ? What is the connection between...

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?

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