Example 7 Show that the function given by f(x) = 7x – 3 is increasing on R Solution Let x1 and x2 be any two numbers in R 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