CHAPTER 16 GRADIENTS; EXTREME VALUES; DIFFERENTIALS 16. Find the directional derivative of f(x,y) =…

CHAPTER 16 GRADIENTS; EXTREME VALUES; DIFFERENTIALS 16. Find the directional derivative of f(x,y) = (x - 1)y^e^ty at (0, 1) toward the point (-1,3). 17. Find the directional derivative of f(x,y) = Ax^2 + 2Bxy + Cy^2 at (a, b) toward (b,a) (a) if a gt; b; (b) if a lt; b. 18. Find the directional derivative of f(x,y,z) = z ln(x/y) at (1,1, 2) toward the point (2,2,1). 19. Find the directional derivative of f(x,y, z) = xey - √(1,2 - 2) in the direction of increasing t along the path r(t) = ti + 2cos(t - 1)j - 2e^(-t)k. 20. Find the directional derivative of f(x,y,z) = x^2 + yz - √(3,2) in the direction of increasing t along the path r(t) = (1/2)i + 3j + 0 - (1/2)k. 21. Find the directional derivatives of f(x,y,z) = x^2 + 2xyz - √(z^2) at (1, 1,2) in the directions parallel to the line 2x - 2y = -1 = -3. 22. Find the directional derivatives of f(x,y,z) = e^x cos(yz) at (0, 1, 2) in the directions parallel to the line in which the planes x + y - 2 = 5 and 4x - y - z = 2 intersect. Exercises 23-26. Find the unit vector in the direction in which f increases most rapidly at P and give the rate of change of f in that direction; find the unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction. 23. f(x,y) = ye^x; P(0, 1).

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Видео CHAPTER 16 GRADIENTS; EXTREME VALUES; DIFFERENTIALS 16. Find the directional derivative of f(x,y) =… канала Harry Walsh