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kieth89

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I'm in calc 1 and want to make sure I'm understanding the reason that we find derivatives. From what I understand, a derivative is simply an equation for the rate of change at any given point on the original function. Is that correct? And the tangent line at point (x,y) is obtained by using the x value in the derivative equation to find the slope at that point, and then use the y value along with that slope to create the equation for the tangent line, right?

I'm a bit confused on whether or not the derivative is also an equation for instantaneous velocity at any given point in the function's domain. It seems like it is, but in the previous chapter we were using limits with the [itex]\frac{f(a + h) - f(a)}{a^2}[/itex] formula (I don't know if that's the right word, isn't it less of a formula and more of the definition of a limit?) to find the average and instantaneous velocity. So is the derivative another way to do that? I guess I'm not sure as to what the relationship is between a derivative and a limit, as it seems like last chapter we were focused on limits and now have dropped them for derivatives.. I've got to be missing some key point here.

I'm a bit confused on whether or not the derivative is also an equation for instantaneous velocity at any given point in the function's domain. It seems like it is, but in the previous chapter we were using limits with the [itex]\frac{f(a + h) - f(a)}{a^2}[/itex] formula (I don't know if that's the right word, isn't it less of a formula and more of the definition of a limit?) to find the average and instantaneous velocity. So is the derivative another way to do that? I guess I'm not sure as to what the relationship is between a derivative and a limit, as it seems like last chapter we were focused on limits and now have dropped them for derivatives.. I've got to be missing some key point here.

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