1.2.1 Exercises 1. For f(x, y) = xey, find Vf(x, y) and Vf (2,0) and the rate of change of f at (2,0) when moving in the direction of vector (-2,3).
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- × Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = y²/x, (2, 4) direction of maximum rate of change (in unit vector) = < maximum rate of change =Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) =8xy2, (5,-7) maximum rate of change direction vectorThe temperature at the point (x, y) on a metal plate is T = + y4 Find the direction of greatest increase in heat from the point (1, 4).
- Calculate Duf(− 4, − 4, 1) in the direction of f(x, y, z) − x² + 5xy + 5y² + 3x Round your answer to four decimal places. = = 27-37-k for the function 3yz + 4z²+xz.Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 5. Please explain your steps. Thank you.Find the maximum rate of change of f at the given point and the direction in which f(x, y, z) = 7x + 6y (3, 2, -1) maximum rate of change direction vector occurs. MY NOTES ASK YOUR
- The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and y are measured in centimeters. Find the direction from point P where the temperature increases most rapidly and this rate of increase. T(x, y) = 80 − 3x2 − y2, P(−1, 5)The directional derivative of the functionf (x, y) = -y³ at the point (-3, –2) in the direction of the vector i = (-4, –3).The temperature at the point (x, y) on a metal plate is T= x² y² · Find the direction of greatest increase in heat from the point (1, 5).