# Find the intervals in which the function is (3/2)x^4-4x^3 - 45x^2 + 51 (a) strictly increasing  (b) strictly decreasing. ​

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Find the intervals in which the function is

$f(x) =$ $\frac{3}{2}x^4-$ 4x3 - 45x2 + 51

(a) strictly increasing

(b) strictly decreasing.

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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,∞).