Related Rates and Velocity Review

Front

What is the formula for the volume of a sphere?

Back

V = (4/3)πr³, where V is the volume and r is the radius.

Front

How do you find the rate of change of the volume of a sphere with respect to its radius?

Back

Use the formula dV/dr = 4πr², which is derived from the volume formula.

Front

What is related rates in calculus?

Back

Related rates involve finding the rate at which one quantity changes with respect to another, often using derivatives.

Front

How do you apply the chain rule in related rates problems?

Back

The chain rule is used to relate the rates of change of different variables, allowing you to differentiate implicitly.

Front

What is the relationship between the diameter and radius of a sphere?

Back

The diameter (d) is twice the radius (r): d = 2r.

Front

How do you calculate average velocity from a position function?

Back

Average velocity is calculated as (s(t2) - s(t1)) / (t2 - t1), where s(t) is the position function.

Front

What is the derivative of the position function with respect to time?

Back

The derivative of the position function s(t) gives the velocity function v(t).

Front

How do you find the instantaneous velocity at a specific time?

Back

To find instantaneous velocity, take the derivative of the position function and evaluate it at the given time.

Front

What is the significance of negative rates in related rates problems?

Back

A negative rate indicates that a quantity is decreasing over time, such as the volume of a deflating balloon.

Front

How do you set up a related rates problem?

Back

Identify the quantities involved, establish relationships between them, and differentiate with respect to time.