Then
x1 < x2 ⇒ 7x1 < 7x2  ⇒ 7x1 – 3 < 7x2 – 3 ⇒ f (x1) < f (x2)
Thus, by Definition 1, it follows that f is strictly increasing on R We shall now give the first derivative test for increasing and decreasing functions The proof of this test requires the Mean Value Theorem studied in Chapter 5 Theorem 1 Let  f  be continuous on [a, b] and differentiable on the open interval
(a,b)