This is for optimization (linear programming) class. What does it mean? Please explain verbally with example please.

Example 16: Solve the following optimization problem. min 2=f(@) =ri+15 - 2102. TER? Solution: We first seek stationary points of the objective function. Definition 8. Let f : R" - R. Vector x E R" is said to be a stationary point of f if Vf(x) = 0.Definition 9. Let f : R" - R. The Hessian matrix of f is 82 f 83 F Or1012 82 f 8- f 82 f 812011 Or20In V'f (x) = 8-f 0- f OIn012 0- In We have the Hessian matrix 8- f 82 F 2 Or1012 V'f (x) = = 83 f 0- f 012011 Remark 10. Consider stationary point r E R" of function f. If every eigen- value of V2f(x) is positive (negative) then x is a local minimizer (maximizer) of f. If the eigenvalues are of mixed sign, then x is a saddle point of f