7. Suppose that a hill is described as {(31}, z) E R3 : (Ly, f(:1:,y))} where f($, y) = 11:3 +37 4:17y 2312. Suppose that a climber is located at p =...

Real analysis problem that I need some help with. It is attached as a picture. Thanks!

7. Suppose that a hill is described as {(31}, z) E R3 : (Ly, f(:1:,y))} wheref($, y) = 11:3 +37 —4:17y— 2312. Suppose that a climber is located at p = (1, 2, —14)on the hill and wants to move from p to another location on the hill withoutchanging elevation. In which direction should the climber proceed from p? EX—press your answer in terms of a vector and completely justify your answer.