How do you find f'(x) using the definition of a derivative for f(x)=5.5x^2 - x + 4.2 f(x)=5.5x2x+4.2?

1 Answer
Sep 26, 2015

See the explanation.

Explanation:

f'(x)=lim_(Deltax->0)(f(x+Deltax)-f(x))/(Deltax)

lim_(Deltax->0) (5.5(x+Deltax)^2-(x+Deltax)+4.2-(5.5x^2-x+4.2))/(Deltax)

lim_(Deltax->0) (5.5x^2+11xDeltax+5.5Delta^2x-x-Deltax+4.2-5.5x^2+x-4.2) /(Deltax)

lim_(Deltax->0) (11xDeltax+5.5Delta^2x-Deltax) /(Deltax)=lim_(Deltax->0) (11x+5.5Deltax-1)

f'(x)=11x-1