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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$ is
  • A
    increasing on $R$
  • ✓
    decreasing on $R$
  • C
    neither increasing nor decreasing
  • D
    none of these
✓

Answer

Correct option: B.
decreasing on $R$
(b) : $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$
$
\therefore f^{\prime}(x)=-4+4 x-x^2=-\left(x^2-4 x+4\right)=-(x-2)^2<0
$
for all $x \in R$
Thus, $f(x)$ is decreasing on $R$.

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