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how to find the minimum points of a equation? watch

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    (Original post by DFranklin)
    Fortunately, some of us have a maths education that didn't stop at maths 101.

    What you've written is errant nonsense, note that functions don't even have to be differentiable. So it would be tricky to use differentiation to find local max/mins for y = | x |.for example.

    Also, in terms of distinguishing min/max/inflexion:

    Define f(x) = exp(-1/x^2) (x non zero), f(0) = 0 and also
    g(x) = -exp(-1/x^2) (x non zero), g(0) = 0 and finally
    h(x) = exp(-1/x^2) (x > 0), -exp(-1/x^2) x < 0, h(0) = 0

    Have fun using differentiation to decide whether each of f, g or h have a minimum, maximum or point of inflexion at x = 0.
    Spoiler:
    Show
    f,g,h are all infinitely differentiable at x = 0, and all their derivatives are 0 there.
    Good point, sorry .
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    (Original post by TeeEm)
    Can someone tell me what maths 101 is?
    I think this is it

    "Mathematics 101 is intended for students who wish to upgrade their mathematics skills before or while attending a post-secondary institution. Students who successfully complete Mathematics 101 are generally permitted to pursue courses and programs that would otherwise require Pure Mathematics 30 as a prerequisite or corequisite.From a background of using algebra and algebraic methods to solve mathematics problems, this course then introduces the concept of a ‘function’ of one or more variables. We first study certain important properties of functions, discover how they can be transformed and consider different ways of working with them numerically (in practical terms), algebraically (in abstract theoretical terms) and geometrically (by visual representations). From there, we discuss a variety of kinds or families of functions which are used to represent and solve real-world situations . In short, we may think of MATH 101 as an introductory course in mathematical modeling."

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    (Original post by Mehrdad jafari)
    I think this is it

    "Mathematics 101 is intended for students who wish to upgrade their mathematics skills before or while attending a post-secondary institution. Students who successfully complete Mathematics 101 are generally permitted to pursue courses and programs that would otherwise require Pure Mathematics 30 as a prerequisite or corequisite.From a background of using algebra and algebraic methods to solve mathematics problems, this course then introduces the concept of a ‘function’ of one or more variables. We first study certain important properties of functions, discover how they can be transformed and consider different ways of working with them numerically (in practical terms), algebraically (in abstract theoretical terms) and geometrically (by visual representations). From there, we discuss a variety of kinds or families of functions which are used to represent and solve real-world situations . In short, we may think of MATH 101 as an introductory course in mathematical modeling."

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    thank you
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    (Original post by TeeEm)
    Can someone tell me what maths 101 is?
    (modified) From :http://forum.wordreference.com/threads/101.1999650/

    101 refers to a foundation course at an American college (eg Psychology 101) and is used more generally to mean "elementary".

    It's an insult, which in its most extreme form, I take to mean "God, everyone knows that. How dumb are you?".

    Clive
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    (Original post by cliverlong)
    (modified) From :http://forum.wordreference.com/threads/101.1999650/

    101 refers to a foundation course at an American college (eg Psychology 101) and is used more generally to mean "elementary".

    It's an insult, which in its most extreme form, I take to mean "God, everyone knows that. How dumb are you?".

    Clive
    thanks

    I am trying to learn the language younger people use these days and sometimes I am strugling.
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    (Original post by TeeEm)
    thanks

    I am trying to learn the language younger people use these days and sometimes I am strugling.
    That's a game you will never win if you enter. You will end up looking like a Dad dancing at a wedding. When I use the word "respect" the students look away rather embarrassed.

    I think stochasticking is sufficiently contrite. Please don't ask me to explain what the word "*******" means, though, from one of his earlier posts ...

    Moral: don't mess with DF.
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    (Original post by TeeEm)
    thanks

    I am trying to learn the language younger people use these days and sometimes I am strugling.
    I am 17. If by "the language younger people use" you mean their slang and popular culture references, then don't worry because I don't either. I would suggest Urban Dictionary but I maintain most of those words have never actually been uttered by a human being.
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    (Original post by 16Characters....)
    I am 17. If by "the language younger people use" you mean their slang and popular culture references, then don't worry because I don't either. I would suggest Urban Dictionary but I maintain most of those words have never actually been uttered by a human being.
    Reassuring.
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    Must. Do. Some. Work.
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    (Original post by TeeEm)
    thank you
    No problem!
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    (Original post by cliverlong)
    That's a game you will never win if you enter. You will end up looking like a Dad dancing at a wedding. When I use the word "respect" the students look away rather embarrassed.

    I think stochasticking is sufficiently contrite. Please don't ask me to explain what the word "*******" means, though, from one of his earlier posts ...

    Moral: don't mess with DF.
    I always appreciate advice
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    (Original post by cliverlong)
    (modified) From :http://forum.wordreference.com/threads/101.1999650/

    101 refers to a foundation course at an American college (eg Psychology 101) and is used more generally to mean "elementary".

    It's an insult, which in its most extreme form, I take to mean "God, everyone knows that. How dumb are you?".

    Clive
    Cool! No, not everyone knows what you are trying to say because not everyone cares. By the way, I think you need to waste your time somewhere else, where people would take notice of what you are trying to say.
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    (Original post by cliverlong)
    That's a game you will never win if you enter. You will end up looking like a Dad dancing at a wedding. When I use the word "respect" the students look away rather embarrassed.

    I think stochasticking is sufficiently contrite. Please don't ask me to explain what the word "*******" means, though, from one of his earlier posts ...

    Moral: don't mess with DF.
    Haha yes I am contrite! I meant it to mean elementary.
    Ps : I'm very new to student room.
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    (Original post by cliverlong)
    Not necessarily. I always mean to write this up systematically.

    ...
    I am sure I can write that more clearly but I think the idea is (mostly) correct. I am sure someone will put me right if not.

    The "old boys" were taught a rule of repeated differentiation (fourth, 5th, etc derivatives) to determine the "real nature" of every turning point and the location of sloping P.O.I.s.
    Just as a coda to your excellent exposition (and as one of the "old boys"!), I'd like to add that:

    (i) it often isn't necessary, or efficient - especially for 'nasty' rational functions, to calculuate higher derivatives. The strict definition of a point of inflexion is where the curvature, and hence the second derivative, changes sign, so it may be easiest simply to calculate the 2nd derivative and examine its sign either side of the point of interest;

    (ii) (and related to (i)) you can have functions where f(x) has a point of inflexion BUT f''(x) is NOT zero. Clearly if f''(x) is defined and continuous at the point in question, then the fact that it changes sign means that it must pass through 0 at the point. However, you can have quite simple functions where f''(x) is NOT defined at a point but has different signs either side of the point, so you still have a point of inflexion.

    It's not without good reason that they rarely examine this concept in exams any more
 
 
 
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