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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 $\text{f} (x) = 4x^{3} - 18x^{2} + 27x - 7$ is always increasing on IR.
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Answer

$f(x) = 4x^3 –18x^2 + 27x – 7$
$f’(x) = 12x^2 – 36x + 27$
$= 3(\text{2x - 3)}^{2} \geq 0 \text{ } \forall \text{ x} \text{}\in \text{R}$
$\Rightarrow$ f(x) is increasing on R.

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