Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 3xy + xyz (a) Find the rate of change of the potential at P(5, 2, 5) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?

Q: B A' A is the point (3, 1). Bis the point (a, 11). The gradient of AB is 5/½ 7 4

A:

Q: A model for the velocity v at time t of a certain object falling under the influence of gravity in a…

A: From the solution draw the graph on the direction field.

Q: f(x, y) = 5eª cos y, (a,b) = (0, 7), a. Calculate the directional derivative of f at the point (a,…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: