Answer:
- a) (fx, fy, fz) = (54, 9, 12)
- b) (fx, fy, fz) = (16, 30, 9)
Step-by-step explanation:
a) The partial derivatives of f(x, y, z) = x³yz² are ...
- fx = 3x²yz²
- fy = x³z²
- fz = 2x³yz
At the given point, these are ...
- fx(1, 2, 3) = 3(1²)(2)(3²) = 54
- fy(1, 2, 3) = (1³)(3²) = 9
- fz(1, 2, 3) = 2(1³)(2)(3) = 12
__
b) The partial derivatives of f(x, y, z) = x² -2xy +3xyz² are ...
- fx = 2x -2y +3yz²
- fy = -2x +3xz²
- fz = 3xy
At the given point, these are ...
- fx(3, 1, -2) = 2(3) -2(1) +3(1)(-2)² = 16
- fy(3, 1, -2) = -2(3) +3(3)(-2)² = 30
- fz(3, 1, -2) = 3(3)(1) = 9
