← Multivariable Calculus

How to solve

Critical points solve f_x = 0 and f_y = 0 simultaneously — for a paraboloid there is exactly one.

Steps

  1. Compute f_x and set it to zero.
  2. Compute f_y and set it to zero.
  3. Solve the two one-variable equations.

Example

f = x² − 6x + y² + 4y. Critical point?

  1. f_x = 2x − 6 = 0 → x = 3.
  2. f_y = 2y + 4 = 0 → y = −2.

Answer: (3, -2)

How to type answers

  • Write points like (3, -2)
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