I need help with the complete answer Describe the geometric interpretation of pa
ID: 2850975 • Letter: I
Question
I need help with the complete answer
Describe the geometric interpretation of partial derivative with respect to x of a two variable function z = f(x, y) at a point (x_0, y_0). How is the partial derivative of a two variable function related to the directional derivative of a two variable function? To find the partial derivative f_x, we would treat y like a constant and differentiate f with respect to x. Geometrically, y = y_0 (a constant) represents a plane in three space that intersects the surface z = f(x, y) along some curve C. The partial derivative f_x at (x_0, y_0) is the slope of the curve or slope of the tangent line to the curve C at the point (x_0, y_0, z_0). The tangent line and the curve C are both is the plane y = y_0. The partial derivative with respect to x is considered to be in the x direction which is parallel to the x axis. The partial derivative with respect to y is considered to be in the y direction or parallel to the y axis. The directional derivative has the same meaning as partial derivative, however, the direction of the vertical intersecting plane b determined by some unit vector in the (x, y) plane.Explanation / Answer
I need help with the complete answer Describe the geometric interpretation of pa