Find
f(a), f(a + h), and the difference quotient f(a + h) − f(a)/h where h ≠ 0.
f(x) = 2x2 + 6
f(a) = 2a2 + 6
f(a + h) = 2(a + h)2 + 6
f(a + h) = 2(a + h)(a + h) + 6
f(a + h) = 2(a2 + 2ah + h2) + 6
f(a + h) = 2a2 + 4ah + 2h2 + 6
f(a+h)−f(a)h =(2a2+4ah+2h2+6)−(2a2+6)h =2a2+4ah+2h2+6−2a2−6h =4ah+2h2h =h(4a+2h)h =4a+2h
