Example 10 Find the intervals in which the function f given by f(x) = x2 – 4x + 6 is
(a) increasing
(b)  decreasing
Solution We have
f (x)
= x2 – 4x + 6
or
f ′(x) = 2x – 4
Therefore, f ′(x) = 0 gives x = 2 Now the point x = 2 divides the real line into two
disjoint intervals namely, (– ∞, 2) and (2, ∞) (Fig 6 3) In the interval (– ∞, 2), f ′(x) = 2x
– 4 < 0