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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 $R$
  • B
    strictly increasing on $R$
  • C
    neither strictly increasing nor strictly decreasing on $R$
  • D
    strictly decreasing on $(-\infty, 0)$
✓

Answer

$\begin{array}{l}\text {} f(x)=x^3-3 x^2+12 x-18 \\ \Rightarrow \quad f^{\prime}(x)=3 x^2-6 x+12=3\left(x^2-2 x+1^2\right)+9 \\ =3(x-1)^2+3^2>0 \forall x \in R \\ \Rightarrow \quad f(x) \text { is strictly increasing on } R\end{array}$

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