f(x)=x(squared)+x-3. compute the difference quotient: (f(x+h)-f(x))/h

Answer 1

f(x+h) = (x+h)^2 + x+h - 3
= x^2 + 2xh + h^2 + x + h - 3

then ( f(x+h) - f(x) )/h
= (x^2 + 2xh + h^2 + x +h - 3 - x^2 - x + 3)/h
= ( 2xh + h^2 +h)/h
= h(2x + h + 1)/h
= 2x + h + 1 , h ≠0