Algebra functions

Question

If f(x) = x^2+2x , find f(x+h) - f(x) / h.

How would I substitute f(x)= (x^2+2x) into (x+h) ?

can you please help me ?.

Answer 1

If f(x) = x^2+2x , find f(x+h) - f(x) / h.

f(x+h)=(x+h)^2+2(x+h)=x^2+2hx+h^2+2x+2h

f(x)=x^2+2x

=f(x+h)- f(x) / h

= x^2+2hx+h^2+2x+2h - (x^2+2x) /h

=x^2+2hx+h^2+2x+2h - x^2-2x /h

= 2hx+h^2+2h / h

= h(2x + h +2) / h

=2x+h+2