EXAMPLE 4 Find the derivative of the function f(x) = x2 - 4x + 8 at the number a. SOLUTION From the definition we have f'(a) = lim f(ath) - f(a) h - 0 h - 4(a + h) + 8 - [a2 - 4a + 8] = lim h - 0 h + - 4a - 4h + 8 - a2 + 4a - 8 = lim h - 0 h = lim h - 0 h = lim h - 0