Thus, f is strictlyincreasing for x > −1.
(b) We have,
f(x)= 10 − 6x − 2x2
The point
divides the real line intotwo disjoint intervals i.e.,
In interval
i.e., when
f'(x)=-6-4x>0.
∴ f is strictly increasing for
In interval
i.e., when
∴ f is strictly decreasing for
(c) We have,
f(x)= −2x3 − 9x2 − 12x +1
Points x =−1 and x = −2 divide the real line into three disjoint intervalsi.e.,
In intervals
i.e., when x < −2and x > −1,
∴ f is strictly decreasing for x <−2 and x > −1.
Now, in interval (−2, −1) i.e., when −2 < x <−1,
∴ f is strictly increasing for 
(d) We have,
The point
divides the real line intotwo disjoint intervals i.e., 
In interval
i.e., for
∴ f is strictly increasing for
In interval
i.e., for
∴ f is strictly decreasing for
(e) We have,
f(x)= (x + 1)3 (x − 3)3
The points x =−1, x = 1, and x = 3 divide the real lineinto four disjoint intervals i.e.,
, (−1, 1), (1, 3), and
In intervalsand (−1, 1), 
∴ f is strictly decreasing inintervalsand (−1, 1).
In intervals (1, 3) and, 