4.1 Interpreting Derivatives in Context

Front

What does p'(1) = 100 represent in the context of a factory's production rate?

Back

The rate of producing hats is increasing at a rate of 100 hats per hour per hour at hour 1.

Front

What does R'(3) indicate regarding the water leak from a tank?

Back

The rate of change of the rate at which water leaks from the tank, in gallons per hour per hour, 3 hours after the leak is discovered.

Front

What does H'(24) signify in terms of temperature at an Arctic weather station?

Back

The rate at which the temperature is changing at the end of the 24th hour.

Front

Interpret d'(15) = 650 in the context of Mr. Bean's distance from home.

Back

At 15 minutes, the distance from home is increasing at a rate of 650 meters per minute.

Front

What does P'(2) = 1/2 mean for the population of a city?

Back

The population in 2012 is growing by half a million people per year.

Front

Define the derivative in the context of a function's rate of change.

Back

The derivative represents the instantaneous rate of change of a function with respect to its variable.

Front

What is the significance of a positive derivative value?

Back

A positive derivative indicates that the function is increasing at that point.

Front

What does a negative derivative value indicate?

Back

A negative derivative indicates that the function is decreasing at that point.

Front

Explain the concept of instantaneous rate of change.

Back

The instantaneous rate of change is the value of the derivative at a specific point, representing how fast the function is changing at that point.

Front

What is the relationship between a function and its derivative?

Back

The derivative of a function provides information about the function's slope and rate of change.