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Lecture33

# Lecture33 - Announcements ThisWeek ExtremeValues WorkOn...

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Announcements This Week: ‐ Direc4onal Deriva4ves ‐ Extreme Values Work On: ‐ Prac4ce Problem Set 12 (Now posted)

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The Direc4onal Deriva4ve The slope of the tangent T to the curve C at the point A is called the direc’onal deriva’ve of f at (a,b) in the direc’on of the unit vector u =u 1 i +u 2 j and is denoted by D u f(a,b). A
The Direc4onal Deriva4ve Defini’on : The direc4onal deriva4ve of a func4on f(x,y) at a point (a,b) in the direc4on of a unit vector u =u 1 i +u 2 j is given by provided that the limit exists. D u f ( a , b ) = lim h 0 f ( a + hu 1 , b + hu 2 ) f ( a , b ) h

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The Direc4onal Deriva4ve Example: #19. Find the direc4onal deriva4ve of at the point A(‐2,‐2) in the direc4on of the vector v=‐ i + j. f ( x , y ) = x 2 + y 2
The Direc4onal Deriva4ve Theorem: Assume that f is a differen4able func4on and u =u 1 i +u 2 j is a unit vector. The direc4onal deriva4ve of f at a point (a,b) in the direc4on u is given by D u f ( a , b ) = f x ( a , b ) u 1 + f y ( a , b ) u 2

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The Direc4onal Deriva4ve Example (revisited): #19. Find the direc4onal deriva4ve of at the point A(‐2,‐2) in the direc4on of the vector v=‐ i + j.
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Lecture33 - Announcements ThisWeek ExtremeValues WorkOn...

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