Question

Using the formula lim h approaches 0 f(x+h)-f(x)/h, find the derivative of f(x)=2x^2+4x

Answer 1

just plug and chug:

f(x+h) = 2(x+h)^2+4(x+h)
= 2x^2+4xh+2h^2+4x+4h
now subtract f(x) = 2x^2+4x and you have
4xh+4h+2h^2

Now divide all that by h, and you have

4x+4+2h

lim as h->0 = 4x+4