# Local Extrema

Topic:
Calculus
The Hesse matrix ist given by Theorem Let be a twice differentiable function with grad f(x0,y0) = 0 and be a symmetric matrix then i) det Hess > 0 ∧ a1,1 > 0 ⇒ Hess is positive definite, i. e. in (x0,y0) is a local minimum of f. ii) det Hess > 0 ∧ a1,1 < 0 ⇒ Hess is negative definite, i. e. in (x0,y0) is a local maximum of f. iii) det Hess < 0 ⇒ Hess is indefinite, i. e. in (x0,y0) is a saddle point. Task Move point P and try to find maxima, minima or saddle points. Use functions such as f(x,y) = x*y , f(x,y) = 0.5(x³ + x² - x) - 0.5y² , f(x,y) = sin(x)*sin(y) etc. Hint: You can change the properties of the grid in the xy-plane to distance π or π /2 as needed.