Find the directional derivative of the function at the given point in the specified direction

Find the maximum rate of change of the function at the given point and determine which direction it occurs in

Find the equation of the tangent plane and the normal line to the given surface at the given point

Find the points on the given ellipsoid where the tangent plane is parallel to the given plane

Find the directional derivative of the function given the unit vector and then find its value at the specified point

Find the gradient vector of the given function at the specified point

Find the directional derivative of the function at the specified point in the direction of the specified direction vector

a) Find the gradient of the given function

b) Find the directional derivative of the function at the specified point in the direction of the specified direction vector

A) Find the rate of change of the function at the specified point and in the specified direction

B) In what direction does f have the maximum rate of change? what is this maximum rate or change?

Suppose the temperature at a point in space is given by the following function where T is measured in degrees Celsius x, y, z in meters. In which direction does the temperature increase fastest at the given point and what is this maximum rate of change?

Find the equations of the tangent plane and normal line at the given point to the ellipsoid