Calculus 11.6 (Directional Derivatives and the Gradient Vector) Example For Students

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 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