Session 10: Absolute maxima and minima of a function over closed and bounded domains.

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Hessian matrix, local maxima, local minima

[aviraj]

sir i want to say a big THANKS to you, you don't even waste our time when you write questions on board. Sometimes looks like it don't affect anything but no, it really saves a lot of time of ours !

[prathameshkale]

Thank you so much for providing such valuable knowledge. It really helped me to fully understand the course of MVC. Thank you so muchh!

[kussumanjalin]

Example 1:
Absolute max value =2 at point (1/2, 1/2)
Absolute Min value= -32 at point (1, 0)
Example 2:
Max temp = 9/4 occurs at points (-1/2, (sqrt(3))/2) and (-1/2, (-sqrt(3))/2)
Min Temp = -1/4 occurs at point (1/2, 0)

[mukiljk]

sir i have a doubt, in case 2 ( using boundary points), we don't include boundary points as critical point's, but when ur listing all the points you included the boundary points at last for the square boundary question, why?

[adeshnagrale]

Sir in 2nd homework problem min value occur at -9.25 in two points (5, -2.5) and(4.5, -3).which point is considered as local minima

[THUNDER-kwwq]

Why didnt we use Hessian matrix to check if the points we got are abs max or abs min or saddle pt?

[sagar]

hw1- absolute minima 0 at (0, 0)
absolute maxima 13 at (0, 4) and (2, 4)
hw2-absolute minima -10 at (4, -2)
absolute maxima 71.75 at (-9/2, -3)

[atharvabhomle]

Sir, in first example at (1, 0) value is -32 so it is absolute minima so it should be critical point. But when I used equation in online calculator it only gives (0.5, 0.5) as maxima and (0, 0) as saddle point. Can you please explain?