M 427L Lecture Notes - Lecture 15: Differentiable Function
17 Mar 2020
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311 3 0 and i find all critical values l0xt42yf. 1c. eu 4s l 4 local max local min a b must be a critical value are max"s mins or a. The collection of all local max min are called the extremes. Defy a b is a critical value flag is not differentiable if fix y or. Theorem if fltly has a then at a point. Defn a differentiable function has a saddleqo. nl at a critical valve a b if. Point saddle in every open disk fly. y i fcab f a b flay. Same instructions f x y 2xy 5 2 2y2t4xt4y 4. Dein the discriminate of a function fcny is dis a det fxxfxyfxxfy. ly fxyy f y q fyy function notnumbes theorem suppose f x y its 1st. 2nd partial derivatus continuous throughout a disk centered at a b are then if.
