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

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  • Опубликовано: 25 ноя 2024

Комментарии • 28

  • @aviraj983
    @aviraj983 Год назад +1

    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 !

    • @DrMathaholic
      @DrMathaholic  Год назад +3

      Thank you for such acute observation. 😊😊 I am happy that it helps you people so much 🙏😊

  • @prathameshkale7209
    @prathameshkale7209 Год назад +1

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

    • @DrMathaholic
      @DrMathaholic  Год назад +1

      Welcome..
      Very happy to hear that 😊

  • @kussumanjalin9859
    @kussumanjalin9859 2 года назад +4

    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)

    • @DrMathaholic
      @DrMathaholic  2 года назад +2

      Thank you for your efforts in posting the answer..

  • @sagar2050
    @sagar2050 2 года назад +1

    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)

    • @DrMathaholic
      @DrMathaholic  2 года назад +2

      Thanks for posting your answer..

    • @sanjaygheji1925
      @sanjaygheji1925 Год назад +1

      in hw 1 how to find local maxima ? values of x & y are coming out complex.

    • @thorrr7613
      @thorrr7613 Год назад +1

      hw-1-absolute min at (0,0) is 1 and absolute max at (0,4) and (4,4) is 17
      hw 2-absolute minima at (4,-2) is -10 and absolute maxima at(0,-3) is 9

    • @aviraj983
      @aviraj983 Год назад

      @@thorrr7613 hw-1-absolute min at (0,0) is 1 and absolute max at (0,4) and (4,4) is 17
      hw 2-absolute minima at (5,-5/2) is -18.5 and absolute maxima at(0,-3) is 11

  • @mukiljk7165
    @mukiljk7165 Год назад +1

    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?

  • @sunitarani5770
    @sunitarani5770 2 года назад +3

    V nice👍👏

  • @adeshnagrale4478
    @adeshnagrale4478 2 года назад +3

    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

    • @DrMathaholic
      @DrMathaholic  2 года назад +1

      If that's what the answer is coming then local minima is occurring at 2 points.
      One can have more than one points of local minima

  • @THUNDER-kw3wq
    @THUNDER-kw3wq Год назад +1

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

    • @DrMathaholic
      @DrMathaholic  Год назад +2

      Good question..
      It only tell us about local extremas reason being, when we prove this theorem involving hessian, we use Taylor's theorem and Taylor's theorem is local in nature ( not global)..

    • @THUNDER-kw3wq
      @THUNDER-kw3wq Год назад +1

      @@DrMathaholic Ooh ohkk...Thank you sir👍🏻

  • @atharvabhomle3191
    @atharvabhomle3191 2 года назад +1

    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?

    • @DrMathaholic
      @DrMathaholic  2 года назад +2

      At 6:09 , We get (0.5,0.5) as critical point.
      So at the end you take this point along with the corner points and interior points on the segments..

    • @atharvabhomle3191
      @atharvabhomle3191 2 года назад +1

      @@DrMathaholic So is (1,0) critical point?

    • @DrMathaholic
      @DrMathaholic  2 года назад +1

      @@atharvabhomle3191 no..it's not the interior point..
      At the end we take
      1.Critical points then
      2. interior points from the segments and
      3. the corner points
      Then value of function at these points

    • @atharvabhomle3191
      @atharvabhomle3191 2 года назад +1

      @@DrMathaholic Sir but online calculator gives (0,0) as critical point too on wolframalpha

    • @DrMathaholic
      @DrMathaholic  2 года назад +2

      @@atharvabhomle3191 on wolfram did you give the region is square???