Question

1. Answer True or False for the following questions: (a) A function can have several local minimu in points in a small neighborhood of x*. (b) A function cannot have more than one global minimum point (c) The value of the function having a global minimum at several points must be the same (d) A function defined on an open set cannot have a global minimum (e) The Hessian matrix of a continuously differentiable function can be asymmetric. (f) The Taylor series expansion of a complicated function replaces it with a polynomial function at the point (g) The linear Taylor series expansion of a complicated function at a point is only a good local approximation for the function (h) The quadratic form appears as one of the terms in Taylor's expansion of a function. (i) If the first-order necessary condition at a point is satisfied for an unconstrained problem, it can be a local maximum point for the function. (j) A point satisfying first-order necessary conditions for an unconstrained function may not be a local minimum point (k) A function can have a negative value at its maximum point (1) If a constant is added to a function, the location of its minimum point is changed. (m) If a function is multiplied by a positive constant, the location of the function's minimum point is unchanged (n) If the Hessian of an unconstrained function is indefinite at a candidate point, the point may be a local maximum or minimum.

Answer 1

Answers :

a) False

b) True

c) False

d) True

e) True

f) True

g) False

h) True

I) False

j) False

k) True

l) True

m) False

n) False

Explanation :

Select all traie statements about lithography, ( A function can have several local mininum I points in a small heighborhood of x. - [False (6 A function cannot have more than one A Global minimum point - True] (c) The value of the functions having a global minimum - at several points must be the same -(False - (@A function defined on an open set cannot I have a global minimum - True ... . (@ The Hessian mature of a continuously differentiable function can be symmetric - True (6 The Taylor sesics expansion of a complicated function - replaces it with a polynomial function at the point - [True (9) The linear Taylor series expansion of a complicated : function at a point is only a good local "approximation for the function - [False ( The quadratic term appears as one of the toms in Taylor's expansion of a function - True ( If the first-order to necessary condition at a point is satisfied problems, for an unconstrained it can be local manimum point for the function - False

o A point satisfying first-order necesary condition for an anconstrained function may not be a local minimum point I fale (6) A function can have a negative value at its maximum point - True) (1) If a constant is added to a function, the location of its minimum point is changed - True - (m) If a function is mulsiplied by a positive worstant, the location of the funcion's minimum point is unchanged. - False - (1) If the Hessian g an unconstrained function is indefinite at a candi clate point, the point may be ä local maximam or minimum -(false)