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Entered Answer Preview Result Message -39 -39 correct -(x^3)-4*X"(y^ 2) +z -13 - 4xy' + z correct (-3x2 - 4y, -8xy, 1) correct (-31, -24, 1) correct Z-(31*x+24*y) = 156 z - (31x + 24y) = 156 incorrect This answer is equivalent to the one you just submitted. At least one of the answers above is NOT correct. Consider the function z = f(x, y) = x3 + 4ry. (a) Find f(-3, -1). z = f(-3, -1) = -39 (b) Find a function g(r, 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(r, y, z) = -*^3-4xy^2+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 Ti perpendicular (or normal) to the graph of z = f(x, y) at the point (-3, -1, -39). Write your answer as a row vector of the general form (a, b, c). n = (e) Find an equation for the tangent plane to z = f(x, y) at the point (-3, -1, -39). Enter your answer as an equation. Z-31x-24y=156