Question

The area of the triangle formed by the tangent to the curve $y=\frac{8}{4+x^2}$ at x = 2 on it and the axes is

• A. 2 sq.units
• B. 4 sq.units
• C. 18.sq.units
• D. 16 sq.units

Answer 1

The correct option is B 4 sq.units

$y=\frac{8}{4+x^2}$
$atx=2$
$y=2$
$hencethepo\mathrm{int}(2,4)$
$slope=\frac{-8}{4+x^2}\times 2x$
$slopeat(2,4)=\frac{-1}{2}$
$equationof\tan gentat(2,4)$
$y-1=-\frac{1}{2}(x-2)$
$\Rightarrow x+2y=4$
$henceareaoftriangle=\frac{1}{2}\times 4\times 2$
$=4$