Application of Derivatives — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
$2 x^3-6 x+5$ is an increasing function, if
A
$0 < x < 1$
B
$-1 < x < 1$
✓
$x < -1$ or $x > 1$
D
$-1 < x < -\frac{1}{2}$
✓
Answer
Correct option: C.
$x < -1$ or $x > 1$
Let $f(x)=2 x^3-6 x+5$
On differentiating $\ce{w.r.t. x}$, we get $f^{\prime}(x)=6 x^2-6$
Since, it is increasing function.
$\Rightarrow 6 x^2-6>0 $
$\Rightarrow(x-1)(x+1)>0$
$\Rightarrow x >1 \text { or } x<-1$
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