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Find the Intervals in Which Function F Given by F(X) = 4x3 - 6x2 - 72x + 30 is (A) Strictly Increasing, (B) Strictly Decresing . - Mathematics

Sum

Find the intervals in which function f given by f(x)  = 4x3 - 6x2 - 72x + 30 is (a) strictly increasing, (b) strictly decresing .

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Solution

f(x)  = 4x3 - 6x2 - 72x + 30 

f'(x) = 12 x - 12x - 72

(a) For strictly increasing funciton

f;(x) > 0

12x2 - 12x - 72 >0

x- x - 6 > 0 .

x - 3x +2x - 6>0 

(x - 3) (x + 2) > 0

⇒ x ∈ (-∞ , - 2) ∪ (3 , ∞)

(b) For strictly decreasing function 

f '(x) < 0

12 x- 12x - 72 < 0

x - x-6 < 0

(x + 2 ) (x - 3) < 0

⇒ x ∈ ( -2 , 3 ) 

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