Multivariable Calculus

How to solve

For f = ax + by the gradient is the constant vector (a, b); its magnitude is √(a² + b²).

Steps

  1. Read off f_x = a and f_y = b.
  2. Square both and add.
  3. Take the square root — these drills use Pythagorean pairs.

Example

f(x, y) = 3x + 4y. Find |∇f|.

  1. ∇f = (3, 4).
  2. √(9 + 16) = 5.

Answer: 5

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