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Suppose the Graph Of z=f(x,y)z = f ( x , y )

Question 78

Essay

Suppose the graph of z=f(x,y)z = f ( x , y ) contains the point P(2,−3,3)P ( 2 , - 3,3 ) , and that the tangent plane at P is given by 3x+2y−5z=−153 x + 2 y - 5 z = - 15 .Find fx(2,−3)f _ { x } ( 2 , - 3 ) and fy(2,−3)f _ { y } ( 2 , - 3 ) .

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