Z= = f(x,y) = x² + 5xy³. (a) Find f(3,-3). z=f(3,-3) -396 (b) Find a function g(x, y, z) whose level zero set is equal t

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Z F X Y X 5xy A Find F 3 3 Z F 3 3 396 B Find A Function G X Y Z Whose Level Zero Set Is Equal T 1 (27.44 KiB) Viewed 23 times

Z= = f(x,y) = x² + 5xy³. (a) Find f(3,-3). z=f(3,-3) -396 (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z=f(x, y) and such that the coefficient of z in g(x, y, z) is 1 The level set g(x, y, z) = -0 is the same as the graph of z = f(x,y). (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c). Vg(x, y, z) = (d) Use Vg to find a vector i perpendicular (or normal) to the graph of z = f(x, y) at the point (3,-3,-396). Write your answer as a row vector of the general form (a, b, c). (e) Find an equation for the tangent plane to z=f(x, y) at the point (3,-3,-396). Enter your answer as an equation.