Consider the function . If is the length of interval of decrease and be the length of interval of increase, then is ____.

JEE MainMathematicsModerateApplication of derivatives

Consider the function
$f(x) = x + \frac{1}{x},x \in (\frac{1}{2},\frac{9}{2})$ . If $\alpha$ is
the length of interval of decrease and $\beta$ be the length of interval
of increase, then $\frac{\beta}{\alpha}$ is ____.

Show answer and solution

f(x) = x + \frac{1}{x},x \in (\frac{1}{2},\frac{9}{2})

is
decreasing in

(\frac{1}{2},1)

and increasing in

(1,\frac{9}{2})

\alpha = 1 - \frac{1}{2} = \frac{1}{2},\beta = \frac{9}{2} - 1 = \frac{7}{2}

\therefore\frac{\beta}{\alpha} = 7

Source: Grass-G / M-20 Mathematics Paper 12 Dec.docx

Scan any doubt from your notes and get a whiteboard explanation.