(Solved): Consider the function Z= f(x, y) = x3 + 4xy = (a) Find f(1, 4). z= = f(1,-4) = = (b) Find a fun ...

Consider the function Z= f(x, y) = x3 + 4xy = (a) Find f(1, –4). z= = f(1,-4) = = (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) - O 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 ñ perpendicular (or normal) to the graph of z = f(x, y) at the point (1, -4,65). Write your answer as a row vector of the general form (a,b,c). ñ (e) Find an equation for the tangent plane to z = f(x, y) at the point (1, -4,65). Enter your answer as an equation.