# Critical Points (Local Maximum, Local Minimum, Saddle Points)

(a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f = 0)

(b) Classify the critical point of f as local maximum, local minimum or saddle points.

See the attached file.

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:35 pm ad1c9bdddfhttps://brainmass.com/math/optimization/critical-points-local-maximum-local-minimum-saddle-points-30746

#### Solution Preview

Please see attached file

Q (a) Find all the critical points of f = xy + yz - zx + xyz (Hint: set f '= 0)

Grad f = i(y -z + yz) + j(x + z + xz) + k(y - x + xy) = 0

Therefore,

y - z + yz = 0...(i)

x + z ...

#### Solution Summary

The solution determines the critical points with details provided.

$2.19