7. The temperature at a point (z, y, z) in R³ near a heat source is given by

T(#, y, z)=

144

√13+¹+¹+z²

Where T is measured in °C and z, y in meters.

(A) (1 point) Find the gradient vector at an arbitrary point (x, y, z) (VT(z, y, z)).

(B) (1 point) Find the equation of the level surface where temperature is 18°C; simplify and

describe the surface.

(C) (0.25 points) The heat source is a single point in 3D space; what point is that?

(D) (0.75 points) Let ñ be the unit vector normal to the surface T(x, y, z)= 18 at a point (x, y, z)

on the surface in direction away from the heat source. Given in terms of x, y, and z. Simplify

as much as possible.

(E) (0.5 points) What is the direction of fastest increase in temperature at point (3, 1,4).