Maths Avatarm
Maths Avatarm
  • Видео 253
  • Просмотров 9 409
If f is twice differentiable on I, then f is convex if and only if f''(x)≥0 ∀ x∈I.
In this lecture, we show that if f is twice differentiable on I, then f is convex if and only if f''(x)≥0 ∀ x∈I. @AmitKumar-cg7be
Просмотров: 29

Видео

f is convex if and only if f' is increasing19:27f is convex if and only if f' is increasing
f is convex if and only if f' is increasing
Просмотров 18День назад
In this lecture, we show that if f:I→R is a differentiable function, then f is convex if and only if f' is increasing on I. @AmitKumar-cg7be
If f is convex, then (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x).16:47If f is convex, then (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x).
If f is convex, then (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x).
Просмотров 26День назад
If f:I→R be a convex function, then for a,b,x∈I with a strictly less than x strictly less than b, we have (f(x)-f(a))/(x-a)≤(f(b)-f(a))/(b-a)≤(f(b)-f(x))/(b-x). @AmitKumar-cg7be
If f is a convex differentiable at x_0∈I, then f has absolute minimum at x_0 iff f'(x_0 )=0.5:21If f is a convex differentiable at x_0∈I, then f has absolute minimum at x_0 iff f'(x_0 )=0.
If f is a convex differentiable at x_0∈I, then f has absolute minimum at x_0 iff f'(x_0 )=0.
Просмотров 20День назад
In this lecture, we show that if f:I→R is a convex function differentiable at x_0∈I, then f has absolute minimum at x_0 if and only if f'(x_0 )=0. @AmitKumar-cg7be
If f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I.8:37If f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I.
If f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I.
Просмотров 22День назад
In this lecture, we show that if f:I→R is a convex function differentiable at x_0∈I, then f'(x_0)(x-x_0)≤f(x)-f(x_0 ) ∀ x∈I. @AmitKumar-cg7be
For a convex function, a point of local minimum is the point of absolute minimum.14:37For a convex function, a point of local minimum is the point of absolute minimum.
For a convex function, a point of local minimum is the point of absolute minimum.
Просмотров 2814 дней назад
In this lecture, we show that for a convex function, a point of local minimum is the point of absolute minimum. @AmitKumar-cg7be
Convex functions and examples29:30Convex functions and examples
Convex functions and examples
Просмотров 2414 дней назад
In this lecture, we define convex functions and also give examples of some of convex functions. @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏.6:57Determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏.
Determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏.
Просмотров 1314 дней назад
In this, we determine all the asymptotes of the curve 𝒚=𝒆^(𝟐/𝒙)−𝟏. @AmitKumar-cg7be
How many horizontal asymptotes can the graph of a given rational function have?7:32How many horizontal asymptotes can the graph of a given rational function have?
How many horizontal asymptotes can the graph of a given rational function have?
Просмотров 1214 дней назад
In this, we discuss, How many horizontal asymptotes can the graph of a given rational function have? @AmitKumar-cg7be
Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero?3:34Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero?
Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero?
Просмотров 2314 дней назад
In this, we discuss, Can the graph of rational function 𝒇(𝒙)/𝒈(𝒙) have an asymptote if 𝒈(𝒙) is never zero? @AmitKumar-cg7be
Let 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. What is l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) ?11:36Let 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. What is l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) ?
Let 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. What is l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) ?
Просмотров 1414 дней назад
In this, we find l𝐢𝐦 𝒙→−∞ 𝒇(𝒙)/𝒈(𝒙) if 𝒇(𝒙) and 𝒈(𝒙) are polynomials such that 𝐥𝐢𝐦 𝒙→∞ 𝒇(𝒙)/𝒈(𝒙) =𝟐. @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙+𝟏).3:59Determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙+𝟏).
Determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙+𝟏).
Просмотров 1221 день назад
In this, we determine all the asymptotes of the curve 𝒚=(𝒙^𝟐−𝒙−𝟐)/(𝒙^𝟐−𝟐𝒙 𝟏). @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=(𝒙+𝟑)/(𝒙+𝟐).2:58Determine all the asymptotes of the curve 𝒚=(𝒙+𝟑)/(𝒙+𝟐).
Determine all the asymptotes of the curve 𝒚=(𝒙+𝟑)/(𝒙+𝟐).
Просмотров 821 день назад
In this, we determine all the asymptotes of the curve 𝒚=(𝒙 𝟑)/(𝒙 𝟐). @AmitKumar-cg7be .
Determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑).2:49Determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑).
Determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑).
Просмотров 1621 день назад
In this, we determine all the asymptotes of the curve 𝒚=−𝟑/(𝒙−𝟑). @AmitKumar-cg7be
Determine all the asymptotes of the curve 𝒚=√𝒙+𝟒/√(𝒙+𝟒).6:20Determine all the asymptotes of the curve 𝒚=√𝒙+𝟒/√(𝒙+𝟒).
Determine all the asymptotes of the curve 𝒚=√𝒙+𝟒/√(𝒙+𝟒).
Просмотров 1021 день назад
In this, we determine all the asymptotes of the curve 𝒚=√𝒙 𝟒/√(𝒙 𝟒). @AmitKumar-cg7be
Determine all the asymptotes of the curve y=(1-x^2)/(x^2+1).15:12Determine all the asymptotes of the curve y=(1-x^2)/(x^2+1).
Determine all the asymptotes of the curve y=(1-x^2)/(x^2+1).
Просмотров 2621 день назад
Determine all the asymptotes of the curve y=(1-x^2)/(x^2 1).
Determine all the asymptotes of the curve y=(x^2+4)/(x-3).16:53Determine all the asymptotes of the curve y=(x^2+4)/(x-3).
Determine all the asymptotes of the curve y=(x^2+4)/(x-3).
Просмотров 1421 день назад
Determine all the asymptotes of the curve y=(x^2 4)/(x-3).
Determine all the asymptotes of the curve y=(x^2+x-6)/(x^2+2x-8).18:47Determine all the asymptotes of the curve y=(x^2+x-6)/(x^2+2x-8).
Determine all the asymptotes of the curve y=(x^2+x-6)/(x^2+2x-8).
Просмотров 921 день назад
Determine all the asymptotes of the curve y=(x^2 x-6)/(x^2 2x-8).
Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)1:03:24Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 1721 день назад
Oblique asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)28:27Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 5021 день назад
Vertical asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)33:00Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Просмотров 2221 день назад
Horizontal asymptotes of an algebraic curve f(x,y)=0 not solvable explicitly as y=g(x) or x=h(y)
Asymptotes of a curve given in polar form24:32Asymptotes of a curve given in polar form
Asymptotes of a curve given in polar form
Просмотров 2221 день назад
Asymptotes of a curve given in polar form
Asymptotes of a curve given in parametric form29:16Asymptotes of a curve given in parametric form
Asymptotes of a curve given in parametric form
Просмотров 1328 дней назад
Asymptotes of a curve given in parametric form
Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)42:10Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)
Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)
Просмотров 2228 дней назад
Asymptotes of a curve g(x,y)=0 solvable explicitly as y=f(x)
Definition of Asymptotes of Curves and its types22:20Definition of Asymptotes of Curves and its types
Definition of Asymptotes of Curves and its types
Просмотров 27Месяц назад
Definition of Asymptotes of Curves and its types
f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.8:21f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.
f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.
Просмотров 13Месяц назад
f'(x) is negative ∀ x∈(a,b), then f is strictly decreasing on [a,b] but converse is not true.
If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.12:25If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.
If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.
Просмотров 15Месяц назад
If f'(x) is positive ∀ x∈(a,b), then f is strictly increasing on [a,b] but converse is not true.
f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)6:49f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)
f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)
Просмотров 22Месяц назад
f is monotonically decreasing/decreasing on [a,b] if and only if f'(x)≤0 for all x∈(a,b)
f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)12:36f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)
f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)
Просмотров 46Месяц назад
f is monotonically increasing/increasing on [a,b] if and only if f'(x)≥0 for all x∈(a,b)
cos⁡x strictly less than (sin⁡x/x)^3 for all x∈(0, π/2)10:56cos⁡x strictly less than (sin⁡x/x)^3 for all x∈(0, π/2)
cos⁡x strictly less than (sin⁡x/x)^3 for all x∈(0, π/2)
Просмотров 24Месяц назад
cos⁡x strictly less than (sin⁡x/x)^3 for all x∈(0, π/2)

Комментарии

  •  8 дней назад

    Nice 🎉

  • @HarshilVasava-h1v
    @HarshilVasava-h1v 9 дней назад

    Thanks 😅

  •  9 дней назад

    🎉😊👍

  •  15 дней назад

    🎉🎉nice 😊

  •  15 дней назад

    Nice 🎉

  •  16 дней назад

    👍👍👍

  • @AmitKumar-cg7be
    @AmitKumar-cg7be 16 дней назад

    In this lecture, also add that S' is convex subset.

  •  18 дней назад

    Good question 🎉👍

  • @AmitKumar-cg7be
    @AmitKumar-cg7be 18 дней назад

    Also add in posibility (1) that neither vertical nor oblique asymptotes exists.

  • @gyanprakashraj4062
    @gyanprakashraj4062 19 дней назад

    ALMAA HII KAAFII HAIN...😂😂😂

  •  20 дней назад

    Good 🎉👍

  •  20 дней назад

    Good 🎉

  •  21 день назад

    Nice class sir 🎉

  •  21 день назад

    Nice class 🎉😊

  • @harendrahaddyia
    @harendrahaddyia 22 дня назад

    Samjhne me problem ho ta hai

  • @harendrahaddyia
    @harendrahaddyia 22 дня назад

    Sir sound proper nahi aata hai

  •  23 дня назад

    Nice class 😊 🎉

  •  23 дня назад

    Good 🎉 👍

  •  25 дней назад

    Nice class ❤🎉

  •  29 дней назад

    Good 👍👍👍

  •  29 дней назад

    Nice 🎉

  •  Месяц назад

    Nice class 👍

  •  Месяц назад

    Nice class 🎉😊

  •  Месяц назад

    Good

  •  Месяц назад

    Nice class

  • @sumittete2804
    @sumittete2804 Месяц назад

    Hello Sir, could you please make a video on how to prove that the total number of subgroups of dihedral group is τ(n) + σ(n)

  • @confusecreation5780
    @confusecreation5780 Месяц назад

    SUC 2 mei jo problem likha hai uska answer to btake jao..😂😂

  •  Месяц назад

    Good question 👍

  • @sairamana5943
    @sairamana5943 Месяц назад

    keep it up

  •  Месяц назад

    Nice 🎉

  •  Месяц назад

    Good 👍

  • @SanjeevTripathi-f6m
    @SanjeevTripathi-f6m Месяц назад

    More videos

  • @SanjeevTripathi-f6m
    @SanjeevTripathi-f6m Месяц назад

    More videos

  • @bikashdutta2585
    @bikashdutta2585 Месяц назад

    🙏

  •  Месяц назад

    Nice class 🎉❤

  • @Iamakash_01
    @Iamakash_01 Месяц назад

    Love from nit delhi electrical❤

  •  Месяц назад

    Nice class 🎉😊

  •  Месяц назад

    Nice explanation 🎉

  • @bikashdutta2585
    @bikashdutta2585 Месяц назад

    🙏

  •  2 месяца назад

    Nice class 😊

  •  2 месяца назад

    Thanks for the class sir Nice class 🎉🎉❤

  •  2 месяца назад

    Nice class ❤

  •  2 месяца назад

    Nice class sir 🎉😊 Thanks for the class 🙏

  •  2 месяца назад

    Good class 😊🎉

  •  2 месяца назад

    👍👍😊

  • @AmitKumar-cg7be
    @AmitKumar-cg7be 2 месяца назад

    In group G, read a^2=b^2=c^2=-I instead of a^2=b^2=c^2=I.

    • @sumittete2804
      @sumittete2804 Месяц назад

      @@AmitKumar-cg7be Hello Sir, could you please make a video on how to prove that the total number of subgroups of dihedral group is τ(n) + σ(n)

    • @AmitKumar-cg7be
      @AmitKumar-cg7be Месяц назад

      I will make.

  • @prince_thakran
    @prince_thakran 2 месяца назад

    ❤

  •  2 месяца назад

    🎉❤😊

  •  2 месяца назад

    Nice class ❤

  •  2 месяца назад

    Nice class sir ji😊🎉