Sum

Find the intervals in which function f given by f(x) = 4x^{3} - 6x^{2} - 72x + 30 is (a) strictly increasing, (b) strictly decresing .

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#### Solution

f(x) = 4x^{3} - 6x^{2} - 72x + 30

f'(x) = 12 x^{2 } - 12x - 72

(a) For strictly increasing funciton

f;(x) > 0

12x^{2} - 12x - 72 >0

x^{2 }- x - 6 > 0 .

x^{2 } - 3x +2x - 6>0

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

⇒ x ∈ (-∞ , - 2) ∪ (3 , ∞)

(b) For strictly decreasing function

f '(x) < 0

12 x^{2 }- 12x - 72 < 0

x^{2 } - x-6 < 0

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

⇒ x ∈ ( -2 , 3 )

Concept: Increasing and Decreasing Functions

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