Average rate of change over an interval

Front

What is the average rate of change?

Back

The average rate of change of a function over an interval [a, b] is defined as the change in the function's value divided by the change in the input value, calculated as (f(b) - f(a)) / (b - a).

Front

How do you calculate the average velocity of an object?

Back

Average velocity is calculated by taking the total displacement divided by the total time taken. It can be found using the formula: (h(t2) - h(t1)) / (t2 - t1).

Front

What is the formula for height of an object thrown upward?

Back

The height h(t) of an object thrown upward is often modeled by the equation h(t) = -16t² + vt + h0, where v is the initial velocity and h0 is the initial height.

Front

What does a negative average velocity indicate?

Back

A negative average velocity indicates that the object is moving in the opposite direction to the positive direction defined in the problem.

Front

What is the significance of the interval in average rate of change?

Back

The interval [a, b] is crucial as it defines the specific time period over which the average rate of change is calculated.

Front

How do you find the average speed from a distance function?

Back

Average speed can be found by calculating the total distance traveled divided by the total time taken, using the formula: (d(t2) - d(t1)) / (t2 - t1).

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Front

What is the average rate of change from [1, 5] for the function f(x) = 2x + 1?

Back

The average rate of change is (f(5) - f(1)) / (5 - 1) = (11 - 3) / 4 = 2.

Front

What does the term 'displacement' refer to?

Back

Displacement refers to the change in position of an object, calculated as the final position minus the initial position.

Front

How do you interpret the average rate of change in a real-world context?

Back

The average rate of change can represent speed, growth rate, or any change in quantity over time, providing insight into how one variable affects another.