Question

f(x)=xx-x+4 what is f(x+h) - f(x) divided by h

Answer 1

f(x) = x^2 - x + 4

f(x+h) = (x+h)^2 - (x+h) + 4
= x^2 + 2xh + h^2 - x - h + 4

so ( f(x+h) - f(x) )/h
= (x^2 + 2xh + h^2 - x - h + 4 - (x^2 - x + 4)/h
= (x^2 + 2xh + h^2 - x - h + 4 - x^2 + x - 4)/h
= (2xh + h^2 -h)/h
= 2x + h - 1