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Calc III Ch13 Notes_Part18

# Calc III Ch13 Notes_Part18 - Not-ice that y‘ouean...

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Unformatted text preview: Not-ice that y‘ouean decompose” the directional derivative: ID.f(x,y)=(7E< ". ”I“ 7;; (1/ r WI” V&m( )T 47a 1L5}; I. The vector valued ﬁmction ab veha-s many uses in math/science, it is called the C3 mlﬂ 3.: :j M9 W5 Deﬁnition: The gradient of [email protected]' (1;, y): 3i; L + 79"] Note: It is usually referred to as “del f’. - Ex: as .ftmﬂﬁfy , J ﬂ =/5'xy L + 3/ Find the gradient of g(x,y) = xsin(y2) \ 2) iii '7 EVA/£7221 ’LZEX (056/9)! ‘* Alternate form of directional derivative: Y n f (x, y) = V? ( \) { P<31'>/QCI/ a) —= (-2, '7 “K” //-': #4,.6/7 ='\r§—3 #28 Ex: Properties of the gra ' l. are? Vicky) ; (ox “L & it! #2. 3 0-7 ﬂ *1/57; +37%"th If Vf(x, y) =6, then Duf(x, y) = 0 for all u. a. Them of marrow HU'C FEE; g is given by Vf(x,92). b. The maximum value of D; f (x, y) is /Z V 3a“ _. a. The direction of MIA/tum 0th6“ is given by —Vf(x, y). b. The minimum value of D" f (x, y) is '— H V"? II . ...
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