Help me please!!

Question

Given C(x)=2x^2-4x+3 find C(x+h)-C(X)/h

I've been stuck for 40mins please help

Answer 1

C(x)=2x²-4x+3

C(x+h)=2(x+h)²-4(x+h)+3=2(x²+2xh+h²)-4(x+h)+3=2x²+4xh+2h²-4x-4h+3

Thus,

C(x+h)-C(x)=2x²+4xh+2h²-4x-4h+3-(2x²-4x+3)=4xh+2h²-4h

Thus,

C(x+h)-C(x)/h=4xh+2h²-4h/h=4x+2h-4