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Question
Prove that the function given by f (x) = x3 – 3x2 + 3x – 100 is increasing in R.
Solution
It is known that- f (x) = x3 - 3x2 + 3x - 100
`therefore` f'(x) = 3x2 - 6x + 3
= 3 (x2 - 2x + 1)
= 3 (x - 1)2 ≥ 0 for all `x in R`
= 3(x - 1)2 > 0
∀ x ∈ R, f''(x) = positive
Hence, the function f is increasing.
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