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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The function/ defined by $f(x)\, = x^3 - 3x^2 + 5x + 7$, is
  • ✓
    increasing in $R$.
  • B
    decreasing in $R$
  • C
    decreasing in $\left( {0,\infty } \right)$ and increasing in $\left( { - \infty ,0} \right)$
  • D
    increasing in $\left( {0,\infty } \right)$ and decreasing in $\left( { - \infty ,0} \right)$
✓

Answer

Correct option: A.
increasing in $R$.
a
$f(x)=x^{3}-3 x^{2}+5 x+7$

For increasing

$f^{\prime}(x)=3 x^{2}-6 x+5>0$

For decreasing

$f^{\prime}(x)=3 x^{2}-6 x+5<0$

$x \in R$

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