Calculus Test 4

valleystudent84's version from 2015-11-14 20:37


Question Answer
Conditions for Rolles Theorem (3)I = Func MUST cont on the closed interval. II= Func MUST be diff. on the open interval. III= the Y values of the end points MUST be the same
Conditions for Mean value theorem (2)I = Func MUST be continuous on the closed interval. II = Must be diff. on the open interval
Extrema - Define - how to findThe extreme values in a given interval; a max or a min. Only occur at critical numbers but NOT ALL critical numbers are exterma - set second Der. to 0. Must set into original to find coordinate
Critical numbers - define - how to findAny Values that make the first Der. 0 or undefined - set first Der to 0
When the slope of the graph is 0, there is an _Extrema
Critical numbers _ _ the intervals of increasing and decreasingBreak up
1st Der Test - define - processIf the graph is increasing BEFORE a critical number and decreasing AFTER a critical number than that must be a MAX. Opposite is true for MIN - set test points into first Der. and check for sign
Concavity - define - processCurvature of the graph; where f"(x) is + = CU and where f"(x) is - = CD - Set f"(x) = 0 and look for PPOI. Any point where the concavity changes is a Pt of inflection. Set test points into f"(x) between these points to see the behavior
Pts of inflection - DefineAny Pt where the concavity changes
In concavity, where A is a pos. number =Concave UP
In concavity, where B is a neg. number =Concave DOWN
In concavity, where test Pts yield a 0, the behavior is _inconclusive
In a rational equation, set _ equal to 0 to find the AsymptotesDenominator
In a rational equation, set _ and _ equal to 0 to find POINumerator - Denominator
Horizontal and or oblique asymptotes are found how (3 ways)Degree in N is larger than D -> No HA - Degree in D is larger -> Y=0 - degree in N and D are the same -> ratio of leading coefficients
Three cases of lim as approaches ∞ in a rational func.∞ left in D = 0 - ∞ left in N = ∞ - No ∞ left = ratio of constants
what does sin(x)/x = (in infinite limits)0
Newtons MethodX(n+1) = Xn - (Func)/(1-der)