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Question
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Solution
(A) increasing
`f(x)=x^3-3x^2+3x-100, x in R`
`f'(x)=3x^2-6x+3`
`=3(x^2-2x+1)`
`=3(x-1)^2`
Since, (x – 1)2 is always positive x ≠ 1
f'(x) > 0 for all x ∈ R, x ≠ 1
Hence, f (x) is an increasing function, for all x ∈ R, x ≠ 1
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