Calculus 11.6 (Directional Derivatives and the Gradient Vector)

Quiz5: Q5

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

Quiz5: Q6

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

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Quiz6: Q1

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

Quiz6: Q2

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

Chapter11.6: Ex1

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

Chapter11.6: Ex2

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

Chapter11.6: Ex3

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

Chapter11.6: Ex4

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

Chapter11.6: Ex5

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?

Chapter11.6: Ex6

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?

Chapter11.6: Ex7

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

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