Here,
\(f(x) = \) \(\frac{3}{2}x^4-\) 4x3 - 45x2 + 51
Now for critical point f'(x) = 0,
6x(x + 3) (x - 5) = 0
x = 0, - 3, 5
i.e., - 3, 0,5 are critical points which divides domain R of given function into four disjoint sub intervals (- ∞, - 3),(- 3 ,0),(0,5),(5,∞).