Find the intervals in which the function f given by f(x) = x² – 4x+6  is
(a) strictly increasing    (b) strictly decreasing

Here f (x) = x² - 4x + 6
∴  (x) = 2x – 4
f '(x) = 0 gives us 2x – 4 = 0 or x = 2
The point x = 2 divides the real line into two disjoint intervals (– ∞, 2). (2, ∞).

(a) In the interval (2, ∞), f ' (x) > 0
∴   f is strictly increasing in (2, ∞).

(b) In the interval (– ∞, 2), (x) < 0
∴   f is strictly decreasing in (– ∞, 2).
Note: Given function f is continuous at x = 2. which is the point joining the two intervals (– ∞, 2) and (2, ∞). Therefore f is decreasing in (– ∞, 2) and increasing in (2, ∞).