In the interval (– ∞, 2), f ′(x) = 2x
– 4 < 0 Therefore, f is decreasing in this interval Also, in the interval (2,
)
∞ , 
( )
0
f
x >
′
and so the function  f  is increasing in this interval Example 11 Find the intervals in which the function f given by f (x) = 4x3 – 6x2 – 72x
+ 30 is (a) increasing (b) decreasing