simplify (f(x+h)-f(h))/h where f(x)=2x^2+x.

Answer 1

f(x)=2x^2+x
f(x+h) = 2(x+h)^2 + x+h
= 2x^2 + 4hx + 2h^2 + x + h

then (f(x+h)-f(h))/h
= (2x^2 + 4hx + 2h^2 + x + h - (2x^2+x) )/h
= (4hx + 2h^2 + h)/h
= h(4x + 2h + 1)/h
= 4x + 2h + 1 , h ≠ 0

In your next step you will be expected to take the limit of that
expression as h ---> 0
and leading up to derivatives. Fun times ahead! Enjoy the mathemagics.