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Increasing and Decreasing Functions — MATHS STD 12 Science — Question

Rajasthan 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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