Find f(a), f(a + h), and the difference quotient

Question

Find f(a), f(a + h), and the difference quotient f(a + h) − f(a)

h

,

 where h ≠ 0.

f(x) = 5 − 2x + 4x²

f(a)	=
f(a + h)	=
f(a + h) − f(a)
h
=

Answer 1

f(a) = 5 - 2a + 4a²

f(a + h) = 5 - 2(a + h) + 4(a + h)² = 5 - 2a - 2h + 4(a² + 2ah + h²) = 5 - 2a - 2h + 4a² + 8ah + 4h²

f(a + h) - f(a) = 5 - 2a - 2h + 4a² + 8ah + 4h² - (5 - 2a + 4a²) = 5 - 2a - 2h + 4a² + 8ah + 4h² - 5 + 2a - 4a²

= -2h + 8ah + 4h²

f(a + h) - f(a)/h = (-2h + 8ah + 4h²)/h = -2 + 8a + 4h