How do you use the limit definition of derivative to find f'(x) here?

Question

f(x)=x-2x^2

and also when f(x)=1/3x

Answer 1

Hi,
Use the limit definition and substitute into it.
f(x)=-2x²+ x
lim [ f(x+h) –f(x)]/h
h-->0

lim [-2(x+h)² +(x+h) – (-2x²+x)]/h
h-->0

lim [-(2x²-4xh-2h²) +x+h +2x²-x]/h
h->0

lim [-4xh-2h² +h]/h
h->0

lim -4x-2h+1
h->0
=-4x +1

FE