Stuff You Must Know Cold - Curve Sketching and Analysis More Derivatives Limits Where u is a function of x and Notation for: a is a constant Limit from the left of f(x) as Critical Points: x -> a - ( x " ) = nx n - 1 Global Min: dx Limit from the right of f(x) as d (sinu) = cosx x -> a dx Global Max: d -(cosu) = - sin x dx Limits you should know: sin x Point of Inflection: d -(tanu) = sec lim X x-0 dx d (cotu) = -csex Derivatives dx 1 - COS x lim d x-+0 (secu) = secx tanx Definition of Derivative dx d (f ( x ) ) = (cscu) = -escx cotx Definition of Continuity: dx dx A function is continuous at the point d I du x = a if and only if: dx (Inu) = u dx d 1. -(eu) = e" du dx dx Alternate Form of Def. of Derivative d a ( f ( x ) ) at x = a dx - (sin 1 u) =- du 71 - udx 2. dx d dx (cos -1 u) = -- d 71 - 92 (tan fu) = du dx Chain Rule d dx - If ( u ) ] = dx (cot ] u) =_ Situations Limits Fail to Exist d 1 + us 1. dx (f - 1 (x) ) = 2. Product Rule 3. a ( uv ) = dx Definition of Vertical Asymptote Situations Derivatives Fail to Exist Quotient Rule 1. d u Definition of Horizontal 2. ax Vi Asymptote 3 Where u and v are functions of x