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## Homework Statement

If you have a point at x = c and a function f(x), then I know Δy = f(c + Δx) - f(c).

Also, dy = f'(c)dx. However, I am uncertain of the origin of dy = f'(x)dx.

I want to say:

f(c + Δx) - f(c) = f'(c)(x-c) was simplified to dy = f'(c)dx

where f(c + Δx) - f(c) = dy

(x-c) = dx

But that would result in Δy = f'(c)dx and Δy > dy. Hence, it is...or should be wrong. Could anybody clairify the origin of dy = f'(c)dx for me?

## Homework Equations

Im the problem, actually.

## The Attempt at a Solution

Also, in the problem! lol