Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x, y) is T(x, y). T(x, y) = 2,400 4x% 2y2, P(2, 2) The surface of a mountain is modeled by the equation h(x, y) = 5,000 0.001x2 0.004y2. A mountain climber is at the point (900, 900, 950). In what direction should the climber move in order to ascend at the greatest rate? Consider the following function and point. Function Point fix,y,2)=\\/x*+y2+22 | (7,5, 4) Find the gradient of the function at the given point. VA7, 5, 4) = Find the maximum value of the directional derivative at the given point