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Question
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Solution
f(x) = x4 − 2x3 + 1
∴ f'(x) = 4x3 - 6x2 = 2x2 (2x - 3)
f(x) is a decreasing function, if f'(x) < 0
∴ 2x2 (2x - 3) < 0
As x2 is always positive,
(2x - 3) < 0
∴ 2x < 3
∴ x < `3/2`
Thus, f(x) is a decreasing function for x <`3/2`, i.e. `(- ∞, 3/2)`.
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