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Math Help - Gradient of curve

  1. #1
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    Gradient of curve

    Hi!

    How many methods are there of finding the gradient of a point on a curve? And can someone pleeeease explain them to me, I tried looking at books and the internet, but it's just all so confusing, I don't understand a word of it! This is for an extension thing at school, so I don't know any thing about calculus...

    Help would be appreciated!

    Suzanna
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Susan111
    Hi!

    How many methods are there of finding the gradient of a point on a curve? Suzanna
    there are no methods for finding the gradient of a point on a curve but methods are there for finding the gradient of a curve at a point.
    One of the methods which I know is finding dy/dx when curve is defined in terms of x and y.
    There are many methods for finding dy/dx
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  3. #3
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    Quote Originally Posted by Susan111
    Hi!

    How many methods are there of finding the gradient of a point on a curve? And can someone pleeeease explain them to me, I tried looking at books and the internet, but it's just all so confusing, I don't understand a word of it! This is for an extension thing at school, so I don't know any thing about calculus...
    Help would be appreciated!
    Suzanna
    Hello,

    I presume that you never have done calculus in school. I further presume that you know to calculate the slope of a line if there are given two points of the line.

    The same method is used to calculate the slope of a chord, connecting two points which belong to a graph of a function. (Look at the 1rst attached diagram). If the point A has the coordinates A(x_0, f(x_0)) and B(x_1,f(x_1)) then you get:

    m=\frac{f(x_1))-f(x_0))}{x_1-x_0} or more shortly: m=\frac{\Delta(f)}{\Delta x}.

    Now imagine that the point B approaches the point A. That means that the \Delta x is approaching zero. The slope of the chord is approaching the slope of the tangent in point A at the graph of the function f. The slope of the tangent in A is called the gradient of f in A. (look at the 2nd attached diagram)

    What I've described (roughly!) in words you can calculate:

    \lim_{\csub{\Delta x \to 0}}{\frac{\Delta(f)}{\Delta x}}=\frac{d(f)}{dx}=f'(x).

    This quotient is called the 1rst derivative of f. It is a function which gives the value of the gradient for every value of x.

    I don't know if you asked for this explanation. If so, I hope this is of some help for you.

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Gradient of curve-slope1.gif   Gradient of curve-slope2.gif  
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  4. #4
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    Thanks so much for your help!
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