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What are derivatives and integrals? 
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#1
Nov2007, 10:30 AM

P: 70

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
Nov2007, 10:36 AM

P: 176

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. 


#3
Nov2007, 10:41 AM

P: 70




#4
Nov2007, 08:31 PM

HW Helper
P: 3,348

What are derivatives and integrals?



#5
Nov2107, 12:24 AM

HW Helper
P: 1,391

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. 


#6
Nov2107, 01:52 AM

P: 70

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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