Suppose you are climbing a hill whose shape is given by the equation z=100 – 0.05x^2 – 0.1y^2, where x,y and z are measured in meters, and you are standing at a point with coordinates (60, 50, 1100). The positive x-axis points east and the positive y-axis points north. If you walk due south, will you start to ascend or descend? At what rate?
The question aims to find the direction if the person starts to walk to the south, whether the person will ascend or descend, and at what rate. This question is based on the concept of directional derivatives. The directional derivative is the dot product of the gradient of the function with its unit vector. Expert Answer […]