**Here,**

** ****\(f(x) = \)** **\(\frac{3}{2}x^4-\)** 4x^{3 }- 45x^{2} + 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,∞).**