You are a small burrowing animal who makes his home under a large rock. Suppose this rock is located at the origin of a 3-dimensional Cartesian coordinate system. In this coordinate system, you are currently located at position (1,2,1). Suppose further that the density of the earth underground is given by the formulaf(x, y, z)= 1/(x² +y²+z²)

(a) Compute the general expression for f

(b) If you were to burrow in the direction(0, 0, 1)how fast would the density of the earth change?

(c)Since you want a challenge, you choose to burrow in the direction that the density of the earth increases the most. What direction is this?

(d)Suppose you instead wish to burrow in a direction where the density remains constant. If you also do not want to change your depth underground (that is, the z-coordinate should continue to be 1), give a direction you would dig.