3 Written Questions
3 Multiple Choice Questions
- A generalization of Rolle's Theorem. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), then there exists one c on (a, b) such that f'(c) = [f(b) - f(a)] / (b-a)
- How fast f(x) is increasing or decreasing at the point x = a
- Suppose two functions f(x) and g(x) are differentiable around a and g'(x) does not equal zero, Then iff trying to find the limit as x approaches a of f(x)/g(x) and the limit of f(x) and g(x) both equal zero, or both equal infinity, then the limits of indeterminate form can be evaluated by taking the derivative of both f(x) and g(x).
2 True/False Questions
Definition of Continuity → If the limit as h approaches zero of [f(a+h) - f(a)] / h exists, then the limit is differentiable at x=a. Notation: f'(a)
Average Rate of Change → [f(b) - f(a)] / (b-a)