Given f(x)= -4x² +3x. Find f(x) using the definition

Question

Precalc help please for homework

Answer 1

I'm going to assume you meant to say "Find f '(x)":

 

f '(x) = lim as h→0 [f(x+h) - f(x)]/h

        = lim as h→0 [-4(x+h)²+3(x+h)+4x²-3x]/h

        = lim as h→0 [-4x²-8hx-4h²+3x+3h+4x²-3x]/h

        = lim as h→0 [-8xh - 4h² + 3h]/h

        = lim as h→0 [-8x - 4h + 3]

        = -8x + 3