Maximum Change Rate Step by step Solution with Explanation

Your question:

Find the maximum rate of change of f(x,y)=ye^(xy) at (x,y)=(0,2) and the direction in which it occurs..

Maximum Change Rate Answers and Explanation

Finding the Maximum Rate of Change and Direction

For f(x, y) = ye^(xy):

∂f/∂x = ye^(xy) * y = y^2 * e^(xy) ∂f/∂y = e^(xy) + xye^(xy) = (1 + x) * ye^(xy)

||∇f(0, 2)|| = ||(4, 2)|| = √(4^2 + 2^2) = √20 = 2√5

Therefore: