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Define instantaneous rate of change.

The rate of change of a function at a specific point in time.

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Define instantaneous rate of change.

The rate of change of a function at a specific point in time.

What does f′(x)f'(x) represent?

The instantaneous rate of change of f(x)f(x) with respect to xx.

What are the units of f′(x)f'(x)?

Units of f(x)f(x) divided by units of xx.

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

f′(t)f'(t)

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

L′(t)L'(t)

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

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

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

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

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

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