MAC 2283 Study Guide - Midterm Guide: Taxco, Parametric Equation, Fxx
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14. 3 partial derivatives . f-xcx, 2) = flex. I f-xycx. lk#,fcx27fxyz=fxzy=fyxz=fyzx=fzxy=fzyx ex ) f ( x. y ) = x" txt y " 222 f- x ( x, 27=3 2+2 23 f- y ( x . X u . l ) slope of tangent line : f x ( lol ) U (cid:195) harmonic functions. ex) ucx. gl = ex sing. Uxx = ex sing uy= ex cosy uyy= - exsing (cid:195) uxxtuyy = o. Du f-( xo , lo ) = thy tcxotha. yothhbl-fcxo. ge ( u = la , b ) ) =3 max of 10 fcx. gl/ when 0=0 (of ku) (cid:195) min of 10 f- cx, 911 when a = tc ( of du opposite) Steps : l . fx=o , f- y = o. Find dc x. y: plug in critical point. ex) flex, y ) = 2 722 - 2x l - 8 -22+2. I . fx=4x -2g - 8=0 , ty - (cid:195) 21=5,2--6.
