dV where V = dt y- x x= 2t, y = 5t, and z = t. Use the Chain Rule to find x+z' av dx (Type an expression using x, y, and z as the variables.)

8. The temperature in °C on the surface of a metal plate is given by T(x, y)= 20-4x² - y² , where x and y %3D are measured in inches. a) In what direction from (2,-3) does the temperature increase most rapidly? What is this rate of increase? b) Provide a contour map and draw the vector that indicates the direction of most rapid increase at (2,-3). c) What is the hottest point on the plate? Note that the vector does not point toward the hottest point on the plate. That is because the gradient provides only a local solution to finding a maximum increase.

The question is attached to this post. Please give full solution and explanation to the answer.

2. Find the directional derivative of f(x,y,z) = x²y + yz² at P(1,–1,3) in the direction of vector (1,5, 2). -2 а) V30 3 b) V30 c) V30 7 d) 30 e) None of the above