Mathematics · Advanced university
Stationary point of a positive-definite quadratic · formula reference
This separable quadratic has positive curvature in each coordinate.
Formula
This separable quadratic has positive curvature in each coordinate.
∇f = 0; positive-definite Hessian gives a unique global minimum
Worked example
For f(x,y)=5x² + (-1)x + 2y², find the x-coordinate of the unique global minimizer. Round the final result to 4 decimal places if needed.
Set ∂f/∂x=10x + (-1)=0 and ∂f/∂y=4y=0. The Hessian is positive definite.
0.1
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.