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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES2 Marks
Question
Show that the function $f(x) = x^3 – 3x^2 + 6x – 100$ is increasing on R.
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Answer

$f(x) = x^3 – 3x^2 + 6x – 100$
$f'(x) = 3x^2 – 6x + 6$
$= 3[x^2 – 2x + 2] = 3[(x – 1)^2 + 1]$
$\text{since f}'(\text{x)} > 0 \text{ }\forall \text{ x} \in$ R $\therefore$ f(x) is increasing on R.

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