# 4.1-4.4.txt

 The flashcards below were created by user kariefury on FreezingBlue Flashcards. What makes a function continuous? A limit exists for all f(x) approaching a and the lim at f(x) = f(a) Are all polynomial functions continuous? Yes What are the local min and max? Points where f prime evaluates to zero (ie No slope bc at bottom of pit) What is the derivative of 1 - x? -1 What is the derivative of -5 + 11 - 6x? -6 What is the derivative of x/40? 1/40 What is the integral of 1/sqrt(x)? 2 sqrt(x) How many feet in a mile? 5280 What is the extreme value theorem? if a real-valued function f is continuous in the closed and bounded interval [a,b], then f must attain its maximum and minimum value, each at least once. Can a function have no maximum and minimum values? Yes, x^3 is an example What is Fermat's Theorem? If f has a local max or min at c, and if f'(c) exists, then f'(c) = 0. What is a critical number? A number c in the domain of f such that either f'(c) = 0 or f'(c) does not exist. Is the local min or max always a critical number? Yes What is the closed interval method? (to find absolute max/min) 1. Find values of f at critical points. 2. Find values of f at end points. 3. Largest/smallest wins. What is the Mean Value Theorem? f(b) - f(a) = f'(c)(b-a) At a point(s) the tangent line is parallel to the secant line. When is a function increasing? f'(x) > 0 When is a function decreasing? f'(x) < 0 What is the First Derivative test? A. (f' + to - at c) = (f has loc max at c)B. (f' - to + at c) = (f has loc min at c)C. (f' stays the same at c) = (f does not have min/max at c) If f' is increasing on I what does concavity look like? Concave up :) If f' is decreasing on I what does concavity look like? Concave down :( What is an inflection point? Point where curve switches concavity Authorkariefury ID15037 Card Set4.1-4.4.txt DescriptionLimits and Continuity Updated2010-04-18T15:23:13Z Show Answers