AP Calculus BC - Derivatives

Question

If f(6+h) - f(6) = ah + bh² + ch³, find f'(6) if possible.

Answer 1

f(6+h) - f(6) = ah + bh² + ch³

[f(6+h) - f(6)] / h = a + bh + ch²

Taking the limit as h approaches 0 of both sides, we have f'(6) = a + b(0) + c(0)² = a