posted by superdiver .
How do I solve this using the TERM BY TERM method?
If f(x)= (2x^2 - 5x - 3) / (3-x)
separate the terms:
f(x) = 2x^2/(3-x) - 5x/(3-x) - 3/(3-x)
now use the quotient rule 3 times:
f'(x) = -2x(x-6)/(3-x)^2 - 15/(3-x)^2 - 3/(3-x)^2
However, this is a waste of time, since
(2x^2 - 5x - 3) = (x-3)(2x+1)
so, f(x) = -(2x+1)
f'(x) = -2 as long as x≠3
so, f'(-8) = -2
moral: see whether a function can be simplified before delving into long calculations.