Solve f'(c)*(b-a): Net Change at c

[Kibbel]

Homework Statement

This is my own question. I am trying to understand what

f'(c)*(b-a) exactly means. I know its (deltaY/deltaX)*deltaX, which gives us deltaY, but does that mean its the net change in Y over the entire interval, or just at point c?

 

[hgfalling]

This doesn't inherently mean anything about y or x.

f'(c) is the derivative of f at c; that is:

$$\lim_{h\rightarrow 0} \frac{f(c+h)-f(c)}{h}$$

f'(c) is the slope of a tangent to the graph of f at c.

Now b and a don't inherently mean anything either; they're probably endpoints of some interval. It looks like you're encountering this in the context of the mean value theorem or something like that. Maybe if you gave some more context, we could clarify this.