see attachment- have to do this because i can't figure out how to do the notation in this part sorry... I have no idea where to go with this and probably need quite a bit of help with it--- thanks.
hey - sorry bud i don't get any of that? - the lecture that we had talked for about 15s on this and I really don't understand it. more help would be GREATLY appreciated.
The derivative definition is usually presented using upper-case delta, [itex]\Delta[/itex] rather than lower-case delta, [itex]\delta[/itex] as you have.
It might be helpful to use function notation, letting f(x) = y = x2 - x. The derivative of f at 1 can be written this way:
[tex]\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{\Delta x}[/tex]
The fraction gives the slope of a secant line between (1, f(1)) and (1 + [itex]\Delta x[/itex], f(1 + [itex]\Delta x[/itex])). The numerator gives the vertical change (rise) and the denominator gives the horizontal change (run). As [itex]\Delta x[/itex] approaches zero, the slope of the secant line approaches the slope of the tangent line.
Substitute for f(1) and f(1 + [itex]\Delta x[/itex]) in the limit formula above, simplify, and then take the limit.
If you still don't understand, your text should have an explanation of this and some examples.