Optimization

Concepts

• Critical point of a multivariable function 10 exercisesA critical point of a function f of two variables is a point (a,b) of its domain where the gradient ∇ f is the zero vector or doe…
• Hessian matrix 10 exercisesThe Hessian matrix H of a function f of two variables is the 2×2 matrix of its second-order partial derivatives at a point.
• Second derivative test 10 exercisesThe second derivative test classifies a critical point of f as a minimum, maximum or saddle according to the sign of the discrimi…
• Lagrange multipliers 10 exercisesThe method of Lagrange multipliers finds the extrema of a function f on the curve g=k among the points where the gradient of f is…
• Absolute extrema on a region 10 exercisesThe absolute extrema of a function f on a closed, bounded region D are the minimum m and the maximum M of the values f takes on D.