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  2. AP Calculus
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If f(t)f(t)f(t) represents volume, what represents the rate of change of volume?

f′(t)f'(t)f′(t)

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If f(t)f(t)f(t) represents volume, what represents the rate of change of volume?

f′(t)f'(t)f′(t)

If L(t)L(t)L(t) represents Instagram likes, what represents the rate of change of likes?

L′(t)L'(t)L′(t)

Explain the meaning of a derivative in applied contexts.

The derivative represents the instantaneous rate at which a quantity is changing at a specific moment.

What does H′(t)H'(t)H′(t) represent if H(t)H(t)H(t) is height at time ttt?

The instantaneous rate of change of height with respect to time (velocity).

Why are units important when interpreting rates of change?

Units provide context and meaning to the numerical value of the rate of change.

Steps to find instantaneous rate of change at t=at=at=a.

  1. Find the derivative f′(t)f'(t)f′(t). 2. Evaluate f′(a)f'(a)f′(a). 3. Include units.

How to find the rate of change of Instagram likes at t=5t=5t=5 days?

  1. Find L′(t)L'(t)L′(t). 2. Evaluate L′(5)L'(5)L′(5). 3. Include units (likes per day).

How to find the rate of change of gas volume at t=4t=4t=4 minutes?

  1. Find G′(t)G'(t)G′(t). 2. Evaluate G′(4)G'(4)G′(4). 3. Include units (liters per minute).