Question
Find the intervals in which the function f given by f(x) = 2x3 – 3x2 – 36x + 7 is decreasing.
✓
Answer
It is given that function f(x) = 2x3 - 3x2 - 36x + 7
$\Rightarrow$ f'(x) = 6x2 - 6x + 36
$\Rightarrow$ f'(x) = 6(x2 - x + 6)
$\Rightarrow$ f'(x) = 6(x + 2)(x - 3)
If f'(x) = 0, then we get,
$\Rightarrow$ x = -2, 3
So, the point x = -2 and x = 3 divides the real line into two disjoint intervals, $(-\infty, 2),(-2,3)$ and $(3, \infty)$
So, in interval (-2, 3)
f'(x) = 6(x + 2)(x - 3) < 0
Therefore, the given function (f) is strictly decreasing in interval (-2, 3).
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