Answer True or False 15 F(x)i 2x2 +2x 17 F(x) = x, + 2x1x3-2d+4G-2x2x3 18 F(x) =

Question

Answer True or False 15 F(x)i 2x2 +2x 17 F(x) = x, + 2x1x3-2d+4G-2x2x3 18 F(x) = 2x1+x1x2 +26+3x-2x1x3 19 F(x) =r(+2x2x3 + x1 + 4 20 F(x)-4x + 2x,x)" x + 4x ection 4.4 Optimality Conditions: Unconstrain 21 Answer True or False. is satisfied for an unconstrained 1. If the firs problem, it can be a local maximum point for the function. point satisfying first-order necessary conditions for an unconstrained funct may not be a local minimum point. 3. A function can have a negative value at its maximum point. 4. If a constant is added to a function, the location of its minimum point is chan nction is multiplied by a positive constant, the location of the function minimum point is unchanged. zero, then it is a local maximum point for the function. minimum point is negative. positive semidefinite. 6. If curvature of an unconstrained function of a single variable at the point x* is 7. The curvature of an unconstrained function of a single variable at its local 8. The Hessian of an unconstrained function at its local minimum point must be 9. The Hessian of an unconstrained function at its minimum point is negative definit 10. If the Hessian of an unconstrained function is indefinite at a candidate point, the point may be a local maximum or minimum. Write optimality conditions and find stationary points for the following functions (use anumerical method or a software package like Excel, MATLAB, or Mathematica, if needed to solve the optimality conditions). Also determine the local minimum, local maximum, and inflection points for the functions (inflection points are those stationary points that are neither minimum nor maximum). +4 ???? ?? : ??? ??

Explanation / Answer

1. TRUE

2. TRUE

3. TRUE

4. TRUE (IN GENERAL TRUE, BUT FOR SOME CASES FALSE IF WE TREAT 0 ADDED TO THE FUNCTION)

5. FALSE

6. TRUE

7. FALSE

8. TRUE

9. FALSE

10. TRUE

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