$\"\"$

\

The frequency $\"\"$ of a fire truck siren heard by a stationary observer is $\"\"$ .

\

(a)

\

Find the rate of change of $\"\"$ with respect to $\"\"$ :

\

when the fire truck is approaching at a velocity of $\"\"$ meters per second(use $\"\"$ ).

\

The function is $\"\"$

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The rate of change when the fire truck is approaching at a velocity of $\"\"$ meters per second is $\"\"$ .

\

$\"\"$

\

(b)

\

Find the rate of change of $\"\"$ with respect to $\"\"$ :

\

When the fire truck is away at a velocity of $\"\"$ meters per second (use $\"\"$ ).

\

The function is $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

The rate of change when the fire truck is away at a velocity of $\"\"$ meters per second is $\"\"$ .

\

$\"\"$

\

(a) The rate of change when the fire truck is approaching at a velocity of $\"\"$ meters per second is $\"\"$ .

\

(b) The rate of change when the fire truck is away at a velocity of $\"\"$ meters per second is $\"\"$ .