If given that Curve sketching and analysis y f(x) must be continuous at each: dy dx 0 or undefined.
ln ( ab ) ln a ln b The Fundamental Theorem of Calculus 6 ( a b ) ln a ln b f ( x)dx F (b) F (a) b a Average Rate of Change (slope of the secant line) If the points (a, f(a)) and (b, f(b)) are on the graph of f(x) the average rate of change of f(x) on the interval is f (b) f (a) Differentiation Rules Chain Rule d du f (u f ) dx dx Product Rule d dv du ( uv ) u v dx dx dx Quotient Rule Definition of Derivative (slope of the tangent line) f ( x h) f ( x) f x) lim h h Derivatives d n x ) nx n ( dx d ( sin x ) cosx dx d ( cos x ) x dx d ( tan x ) sec2 x dx d ( cot x ) x dx d ( sec x ) tanx sec x dx d ( csc x ) csc x dx d 1 ( ln u ) du dx u d u e ) eu du ( dx d 1 ( log a x ) dx x ln a d u a ) a x ( ln a ) du ( dx d dx v v du dv dx dx 2 v Mean Value Theorem If the function f(x) is continuous on and the first derivative exists on the interval (a, b), then there exists a number x c on (a, b) such that f c ) f (b ) f ( a ) where F x) f ( x) 2nd Fundamental Theorem of Calculus g ( x) d f ( x)dx f ( g ( x )) g x) dx Average Value If the function f(x) is continuous on and the first derivative exist on the interval (a, b), then there exists a number x c on (a, b) such that b 1 f (c ) f ( x)dx b a f (c) is the average value Method if f(a) f(b), then f 0. Preview text AP CALCULUS BC Stuff you MUST Know Cold Rule f (a ) 0, If or g (a ) 0 f (x) f x ) lim then lim a g ( x) x a g x ) Properties of Log and Ln 1.
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