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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x^3-3 x^2+12 x-18$ is :
  • A
    strictly decreasing on $R$
  • ✓
    strictly increasing on $R$
  • C
    neither strictly increasing nor strictly decreasing on $R$
  • D
    strictly decreasing on $(-\infty, 0)$
✓

Answer

Correct option: B.
strictly increasing on $R$
$\text {} f(x)=x^3-3 x^2+12 x-18$
$\Rightarrow f^{\prime}(x)=3 x^2-6 x+12$
$=3\left(x^2-2 x+1^2\right)+9$
$=3(x-1)^2+3^2>0 \forall x \in R$
$\Rightarrow f(x)$ is strictly increasing on $R$

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