Prove that the function given by f(x) = x^3 - 3x^2 + 3x - 100 is … - Vidyadip

Question

Prove that the function given by $f(x) = x^3 - 3x^2 + 3x - 100$ is increasing in R.

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Answer

Given: $\text{f}\text{(x)} = \text{x}^{3} -3\text{x}^{2} + 3\text{x} -100 $
$ \Rightarrow \ \text{f}'\text{(x)} = 3\text{x}^{2} -6\text{x} + 3 = (\text{x}^2 -2\text{x}+1)$
$\Rightarrow\ \text{f}'\text{(x)} = (\text{x} -1)^{2}\geq 0 $ for all x in R.
Therefore, f(x) is increasing on R.

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