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Question
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 x2 - 12x - 72
(a) For strictly increasing funciton
f;(x) > 0
12x2 - 12x - 72 >0
x2 - x - 6 > 0 .
x2 - 3x +2x - 6>0
(x - 3) (x + 2) > 0
⇒ x ∈ (-∞ , - 2) ∪ (3 , ∞)
(b) For strictly decreasing function
f '(x) < 0
12 x2 - 12x - 72 < 0
x2 - x-6 < 0
(x + 2 ) (x - 3) < 0
⇒ x ∈ ( -2 , 3 )
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