Model Paper 6 — Applied Maths STD 12 Science — Question
CBSE BoardEnglish MediumSTD 12 ScienceApplied MathsModel Paper 61 Mark
MCQ
The function $f ( x )=\frac{x}{2}+\frac{2}{x}$ has a local minimum at
A
$x=-1$
B
$x=-2$
C
$x=2$
D
$x=1$
✓
Answer
(c) $x=2$ Explanation: $f ( x )=\frac{x}{2}+\frac{2}{x} \Rightarrow f ^{\prime}( x )=\frac{1}{2}+\frac{2}{x^2}$ and $f ^{\prime \prime}( x )=\frac{4}{x^3}$ Now, $f^{\prime}(x)=0 \Rightarrow x^2=4 \Rightarrow x= \pm 2$ $ \because f^{\prime \prime}(2)=\frac{4}{2^3}=\frac{1}{2}>0 $ $\Rightarrow f(x)$ has a local minimum at $x=2$
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