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DIFFERENTIATION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsDIFFERENTIATION3 Marks
Question
Determine whether the function $\mathrm{y}=3 \mathrm{x}^2-\mathrm{x}+7$ is increasing or decreasing at $\mathrm{x}=1$ and $\mathrm{x}=2$.
✓

Answer

$y=3 x^2-x+7$
$\therefore \frac{d y}{d x}=3(2 x)-10(1)+0$
$=6 x-10$
At, $x=1 \frac{d y}{d x}=6(1)-10=6-10=-4<0$.
So, at $x=1$ function is decreasing.
At $x=2, \frac{d y}{d x}=6(2)-10=12-10=2 >0$.
So, at $x=2$ function is increasing.

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