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Model Paper 5 — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsModel Paper 52 Marks
Question
Show that the function $f(x)=\frac{x}{3}+\frac{3}{x}$ decreases in the intervals $(-3,0) \cup(0,3)$.
✓

Answer

$f(x)=\frac{1}{3}-\frac{3}{x^2}$
for decreasing $f^{\prime}(x)<0 \Rightarrow \frac{1}{3}-\frac{3}{x^2}<0$
$\Rightarrow x^2$ < 9 $\Rightarrow$ -3 < x < 3
since, f(x) is not defined at x = 0
so $f(x)$ decreasing in $(-3,0) \cup(0,3)$

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