Given fx 2x x2 find and simplify the difference quotient f

Given: f(x) = 2x + x^2 find and simplify the difference quotient: f(x + h) - f(x)/h

Solution

f(x) = 2x +x² , f(x+h) = 2(x+h) + (x+h) ²

f(x+h) - f(x) = 2x+2h+ x²+2xh +h² - 2x -x²

  = 2h+ 2xh +h²

h( 2+ 2x+ h)

[ f(x+h) - f(x) ] /h = 2 + 2x +h

when h-> 0 we get

f \'(x) = 2 +2x