derivative of an equation?

I've got a pretty good grasp on the subject so far, but I'm still confused about some minor details and while the details may be stupid to some, I still want to confirm to make sure I'm not on the wrong yellow brick road.

When you don't plug in anything for x using the difference quotient, whatever solution you get lets you plug in any x point on the line for that equation to find its deriv. right? like the d for for 5x^ -3x-7 gives me a general solution of 10x-3, so can I then just start plugging in points now? Like for x=3 of the above equation, the derivative is 27 right?

?2010-09-27T12:16:57Z

In your example where the derivative is 10x -3, this is the general derivative. Every point on the curve 5x^2 -3x-7 has a tangent to it. For every value of X we can draw this tangent to the curve and the gradient of this tangent can be found using the general derivative found earlier.

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