The volume and depth of water in a vessel are connected by the relation and the…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The volume

V

and depth

x

of water in a vessel are connected by the relation

V = 5x - \frac{x^2}{6}

and the volume of water is increasing at the rate of

5\,\text{cm}^3/\text{sec}

, when

x = 2\,\text{cm}

. The rate at which the depth of water is increasing, is (a)

\frac{5}{18}\,\text{cm/sec}

(b)

\frac{1}{4}\,\text{cm/sec}

(c)

\frac{5}{16}\,\text{cm/sec}

(d) None of these