Let f(x)=5·x2−2·x. Find
f(x+h)−f(x)/h if h≠0

Question

Let f(x)=5·x2−2·x. Find
f(x+h)−f(x)/h if h≠0

campbell_st · Answer

replace x with (x+h) in every term containing an x

f(x + h) = 5(x+h)^2 - 2(x+h)

expand and simplify    5(x^2 +2xh + h^2) -2x -2h
                                    = 5x^2 + 10xh + 5h^2 -2x -2h

Now f(x+h) -f(x) = 5x^2 + 10xh + 5h^2 - 2x - 2h - 5x^2 - 2x

leaves                   10xh +5h^2 -2h

divide by h
 $$(10xh - 5h^2 -2h)/h = 10x - 5h - 2$$

this is differentiation  from 1st principles...

anonymous · Answer

Thanks, I forgot to substitute one of the x +h. I appreciate the help