Test Index

AP EAPCET 24-Aug-2021 Shift 1 Paper

Section: Mathematics

© examsnet.com

Question : 66 of 160

Marks: +1, -0

If

2 f(x)-3 f\left(\frac{1}{x}\right)=x+1

f'(\sqrt{3})=

______

$-\frac{1}{5}$
$\frac{3}{5}$
$-\frac{\sqrt{3}}{5}$
$\frac{\sqrt{3}}{5}$

Solution:

2 f(x)-3 f\left(\frac{1}{x}\right)=x+1

...(i)

Replace

x \rightarrow \frac{1}{x}

2 f\left(\frac{1}{x}\right)-3 f(x)=\frac{1}{x}+1

...(ii)

Multiply Eq. (i) by 2 and Eq. (ii) by 3 and then adding

4 f(x)-6 f\left(\frac{1}{x}\right)=2 x+2

6 f\left(\frac{1}{x}\right)-9 f(x)=\frac{3}{x}+3

4 f(x)-9 f(x)=2 x+\frac{3}{x}+5

\Rightarrow -5 f(x)=2 x+\frac{3}{x}+5

\Rightarrow f(x)=-\frac{2}{5} x-\frac{3}{5 x}-1

Differentiate w.r.t.

x

,

f'(x)=-\frac{2}{5}+\frac{3}{5 x^{2}}

f'(\sqrt{3})=-\frac{2}{5}+\frac{3}{5(\sqrt{3})^{2}}

=-\frac{2}{5}+\frac{3}{5 \times 3}

=-\frac{2}{5}+\frac{1}{5}=\frac{-2+1}{5}

=-\frac{1}{5}

© examsnet.com

Go to Question:

Prev Question

Next Question