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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 following function are increasing on R.
$f(x) = 4x^3 + 18x^2 + 27x - 27$
✓

Answer

$f(x) = 4x^3 + 18x^2 + 27x - 27$
$\Rightarrow f'(x) = 12x^2 + 36x + 27$
$\Rightarrow f'(x) = 3(4x^2 - 12x +9)$
$\Rightarrow\text{f}'(\text{x})=3(2\text{x}-3)^2>0,\forall\ \text{x}\in\text{R}$
So, f(x) increasing on R.

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