$\"\"$

\

The volume $\"\"$ of the water remaining in the tank after $\"\"$ minutes is $\"\"$ , $\"\"$ .

\

The rate at which water is draining from the tank $\"\"$ is $\"\"$ .

\

Consider $\"\"$ .

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$ .

\

Chain rule of derivatives: $\"\"$ .

\

$\"\"$

\

(a)

\

Rate at which water is draining from the tank after $\"\"$ min :

\

$\"\"$

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

$\"\"$

\

(b)

\

Rate at which water is draining from the tank after $\"\"$ min :

\

$\"\"$

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

$\"\"$

\

(c)

\

Rate at which water is draining from the tank after $\"\"$ min :

\

$\"\"$

\

Her negative sign indicates that the level of the water in the tank was decreases.

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

$\"\"$

\

(d)

\

Rate at which water is draining from the tank after $\"\"$ min is

\

$\"\"$

\

Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

$\"\"$

\

(a) Rate at which water is draining from the tank after $\"\"$ min is

\

$\"\"$ gallons/min.

\

(b) Rate at which water is draining from the tank after $\"\"$ min is

\

$\"\"$ gallons/min.

\

(c) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.

\

(d) Rate at which water is draining from the tank after $\"\"$ min is $\"\"$ gallons/min.