# AP Calculus Chapter 3

 Critical Numbers Values of x in the domain of f (x) where f 'x= 0 or f 'x is undefined How do you find absolute minimums and maximums on a closed interval? 1. Find critical numbers 2. Find values for the function at each endpoint and critical number 3. Determine absolute max and absolute min for the interval by your results from step 2. Rolle’s Theorem If f is differentiable on the interval (a , b) and f(a) = f(b) then there is at least one place in the interval where f 'x= 0 Mean Value Theorem (MVT) If f (x) is continuous and differentiable on the interval [a , b], there is someplace in the interval where f ' x equals the slope of the line going through the endpoints of the interval. First Derivative ITSC 1) Use critical numbers to determine intervals. Interval Test Value Sign of f ' x Conclusion If sign of f ' x is positive what is happening to f(x)? f(x) is increasing If sign of f ' x is negative then f(x) is _______. f(x) is decreasing First Derivative Test Do a first derivative ITSC, If f ' x is changing from pos to neg, then relative max If f ' x is changing from neg to pos, then relative min Concave Up f'(x) is increasing, f''(x)is positive, f(x) will hold water AuthorAnonymous ID109669 Card SetAP Calculus Chapter 3 DescriptionThese are my flashcards for the third chapter of my book, Calculus of a single variable AP edition Updated2011-10-17T21:45:01Z Show Answers