2022年AP微积分CALCULUS知识点总结

1、A DERIVATIVE FUNCTIONThe derivative function or simply the derivative is defined as Find the derivative functionFind ,Find the average rate of change ,Find the limit .Geometric significanceConsider a general function y=f(x), a fixed point A(a,f(a) and a variable point B(x,f(x). The slope of chord AB

2、=. Now as BA, xa and the slope of chord ABslope of tangent at A.So, is .Thus, we can know the derivative at x=a is the slope of the tangent at x=a.RulesC(a constant)0 The chain ruleIf where then . , 6. Inverse function, Parametric function and Implicit functionInverse function:, , i.e., , Parametric

3、 function:, i.e., , Implicit function: , ., , t High derivativey=sinx , B Applications of differential calculusMonotonicity If S is an interval of real numbers and f(x) is defined for all x in S, then： f(x) is increasing on S for all x in S, and f(x) is decreasing on S for all x in S. Find the monot

4、one intervalFind domain of the function,Find , and x which make ,Draw sign diagram, find the monotone interval.Maxima/Minima, Horizontal inflection, Stationary pointC INTEGRALThe idea of definite integralWe define the unique number between all lower and upper sums as and call it “the definite integral of from a to b”,i.e., where .We note that as , and We write .If for all x on a,b then is the shaded area.Properties of definite integrals, c is any constant, where （f(x) odd）,(f(x)even)If on then If on then The average value of a function on an interval a,bThe infinite integralIf ,