$\"\"$

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

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(a)

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

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

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The function is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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(b)

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

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

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The function is $\"\"$ .

\

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

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ .

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

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 $\"\"$ .

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