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Question
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
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Solution
f(x) = 2x3 - 3x2 - 36x + 7
f'(x) = 6x2 - 6x - 36
= 6(x2 - x - 6)
= 6(x - 3) (x + 2)
if, f'(x) = 0
6(x - 3) (x + 2) = 0
x = -2, 3 divides the real line into three intervals `(- infty, - 2), (-2, 3)` and `(3, infty)`.
(a) The function f is continuously increasing in the intervals `(- infty, - 2)` and `(3, infty)`.
(b) The function f is continuously decreasing in the interval (-2, 3).
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