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Increasing and Decreasing Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIncreasing and Decreasing Functions2 Marks
Question
Prove that the function $f(x) = x^3 - 6x^2 + 12x - 18$ is increasing on $R$.
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Answer

$f(x) = x^3 - 6x^2 + 12x - 18$
$f'(x) = 3x^2 - 12x + 12$
$= 3(x^2 - 4x + 4)$
$= 3(\text{x} - 2)^2\geq0,\forall\text{x}\in\text{R}$ $[3>0\ \&(\text{x}-2)^2\geq0]$
So, f(x) is increasing on R.

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