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CSU Pomona - MATH 2140 - Class Notes - Week 9

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CSU Pomona - MATH 2140 - Class Notes - Week 9

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School: California State Polytechnic University - Pomona
Department: Applied Mathematics
Course: Calculus 3
Professor: Randy Swift
Term: Fall 2018
Name: MAT 2140 - week 9
Description: Notes covers the 2nd derivative test, and critical points
Uploaded: 10/29/2018
4 Pages 47 Views 37 Unlocks
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Unformatted text preview: CO ch 14 last time z: flXD) Cacadient: If=<fx fv> Directional Denvative ? The denitine direction of a unit restoy - Lab Do fcorto) = f (xo,ya) -7. Gradient Tack I the gradient vf gives the direction of the po increase of f. 2. is PCXola, Za) is a point the then illo You, Ze) 15 orthogonal to the level surface s off through P You Waze Largent Playe suppose a surfaces has equation Zafelej foxin) hauira continouous partial derivatives Let PCX, Yo, ze) be a point on Then the equation of tre tangent pare to Tetto, Yo, zo] sur lacus torgen Planes ><fon) Z-Zo = fx {X., 4(X-X) +ty loilo C equation of tangent line 7-40fC.) (X-Xo) PExoil ze)hind on egy of the tangent pla Surface Lat (217) Son A (1:2) = 18(1) + = 24 Ny and 27-23 SOSOL 22-(1,2)=212)-3=1 Soy 7-2. = 24 kortb]** *+ 34, tx, *?yyy becomes 7-19-2240X-1) +1(y-2) Z=29-2y y -2 +18 24xty-2=8 Find a vector normal S: <24,1,-17For X ner 10, the forere approxima foil farly well, A similor idea: The torent plare at lave, on the surfa s give by z foy) gives an epoca kimation to the surface The linear approximation br lirearization Laxy) of the surface s. given by oz af(y) o liso, yo, Ze) is IXY) Zet fylkeslo (X-X) fylley) (Y-Y) Llx,y)=f(Xilo tfeleil) + fy (XY) - Yo] Example Find the linear approximation of _fum - en:(X-3y) at (72) 8772) - 17-312) Philo FxW) = x-3y 80, fy 17,21. = 7601 anet + fylxi yl -34 son fyt7.2) 76

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