- #1
tcuay
- 8
- 0
These 2 questions,I have attempted them for hours but still no outcome
For the first question:
part a) i take the ∇f(x) and set it to be zero;
then find out(x1,x2)=(0,-1) or((-2a-1)/3,(-2a-4)/3);
but then for part b), after using second-order necessary condition,
i have no idea to continue;
part c): i know if i can prove the function is convex or concave, i can surely conclude the local minimum/maximum is a global minimum/maximum; but after taking the gradient for 2 times, i don't know to work for it in further;
For Question 2,
part a) i got 5 possible points (x1,x2)=(0.5,0),(1,-1),(1,1),(-1,-sqrt(3)),(-1,sqrt(3));
but in part b) i can only prove (0.5,0) is a local maximizer while other 4 points don't satisfy the 2nd conditions(because their determinant of Hessian Matrix is smaller than zero;)
part c) same, no idea how to do it;
part d) i find the directional vectors are both [0,0]'; does it mean f(1,-1) is a local minimum?
Thanks for help
For the first question:
part a) i take the ∇f(x) and set it to be zero;
then find out(x1,x2)=(0,-1) or((-2a-1)/3,(-2a-4)/3);
but then for part b), after using second-order necessary condition,
i have no idea to continue;
part c): i know if i can prove the function is convex or concave, i can surely conclude the local minimum/maximum is a global minimum/maximum; but after taking the gradient for 2 times, i don't know to work for it in further;
For Question 2,
part a) i got 5 possible points (x1,x2)=(0.5,0),(1,-1),(1,1),(-1,-sqrt(3)),(-1,sqrt(3));
but in part b) i can only prove (0.5,0) is a local maximizer while other 4 points don't satisfy the 2nd conditions(because their determinant of Hessian Matrix is smaller than zero;)
part c) same, no idea how to do it;
part d) i find the directional vectors are both [0,0]'; does it mean f(1,-1) is a local minimum?
Thanks for help