beast - that aint no assumption - ive taken enough calc to show its true. Thats actually pretty much the entire idea behind calculus. Using derivatives, tangent lines, tangent planes, ect to determine values relating to a function. If you limit the domain of a derivative, it will (for all practical purposes) be equal the original function in that domain. you can substitute a for b because they can be equal. Its no different than the sin of theta for small numbers is approximately equal to the tan of theta for small numbers.