Consider the function

z=f(x,y)=x³+6xy².

(a) Find f(2,3). z=f(2,3)= (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)= ANSWER NEEDED =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. g(x,y,z)= ANSWER NEEDED (d) Use g to find a vector n perpendicular (or normal) to the graph of z=f(x,y) at the point (2,3,116). Write your answer as a row vector of the general form a,b,c. n= ANSWER NEEDED (e) Find an equation for the tangent plane to z=f(x,y) at the point (2,3,116). Enter your answer as an equation. ANSWER NEEDED