What are derivatives and integrals?

  1. Nov 20, 2007 #1
    What are they? In my book Im studying limits and it has mentioned a few times before and in the current chapter Derivatives and Integrals, but hasnt explained them. Could anybody explain what these two things are, exactly?
     
  2. jcsd
  3. Nov 20, 2007 #2
    if your asking for a formal definition then goto www.wikipedia.com and search for derivative and separately integration.

    Geometric calculus interpretation:

    If f(x) is a line and can be represented by mx +b then the slope is m, but this is a line and the slope is the same throughout the real numbers. Now consider y= x^2, what is the slope? it changes at each point, the slope at any point is the derivative of the function evaluated at that point.

    the integral of a real function gives you the area under the curve of the function.
     
  4. Nov 20, 2007 #3
    So does this mean that there can be as many derivatives as there are points?
     
  5. Nov 20, 2007 #4

    Gib Z

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    Different functions can be differentiated a different number of times.
     
  6. Nov 21, 2007 #5

    Mute

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    It means that in general the derivative of a function of x is itself a function of x. i.e., the slope of a function is different at each point on that function.

    For example, the derivative of x^2 is 2x. This means that on the curve y = x^2, at the point x = 4, the slope of the curve at x = 4 (or, perhaps more precisely, the slope of the line tangent to the curve at x = 4) is 2*4 = 8. Similarly, the slope at the point x = -5 is -10.
     
  7. Nov 21, 2007 #6
    Ah, thanks for clearing that up for me everybody, that explains it. I think as I'm beginning to learn more about simple calculus I'm beginning to like it more. Haha, it just might turn into a hobby once I learn enough.
     
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