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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f$ defined by $f(x)=4 x^4-2 x+1$ is increasing for
  • A
    $x<1$
  • B
    $x>0$
  • C
    $x<\frac{1}{2}$
  • ✓
    $x>\frac{1}{2}$
✓

Answer

Correct option: D.
$x>\frac{1}{2}$
(d) : We have, $f(x)=4 x^4-2 x+1 \Rightarrow f^{\prime}(x)=16 x^3-2$
The function is increasing if $f^{\prime}(x)>0$
$
\Rightarrow 16 x^3-2>0 \Rightarrow x>\frac{1}{2}
$

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