Let f:R2→R be the function defined by f(x,y)=−(x−4)2−(y−4)2. a) Calculate the critical points of f. b) Calculate the Hessian of f. c) Find the local maximum, local minimum and saddle points of f, if any. Calculate the respective values of f at such points.
Let f:R2→R be the function defined by f(x,y)=−(x−4)2−(y−4)2. a) Calculate the critical points of f. b) Calculate the Hessian of f. c) Find the local maximum, local minimum and saddle points of f, if any. Calculate the respective values of f at such points.
Let f:R2→R be the function defined by f(x,y)=−(x−4)2−(y−4)2. a) Calculate the critical points of f. b) Calculate the Hessian of f. c) Find the local maximum, local minimum and saddle points of f, if any. Calculate the respective values of f at such points.
a) Calculate the critical points of f. b) Calculate the Hessian of f. c) Find the local maximum, local minimum and saddle points of f, if any. Calculate the respective values of f at such points. d) Consider the curve C of R2 described by the equation
Formula Formula A function f ( x ) is also said to have attained a local minimum at x = a , if there exists a neighborhood ( a − δ , a + δ ) of a such that, f ( x ) > f ( a ) , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a f ( x ) − f ( a ) > 0 , ∀ x ∈ ( a − δ , a + δ ) , x ≠ a In such a case f ( a ) is called the local minimum value of f ( x ) at x = a .
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