Unit 4 Review

Front

What does it mean when a particle's velocity and acceleration have opposite signs?

Back

The speed of the particle is decreasing.

Front

What is the formula for the volume of a sphere?

Back

Front

What is linear approximation?

Back

A method to estimate the value of a function near a given point using the tangent line.

Front

What does it indicate if a function is concave down?

Back

The second derivative of the function is negative, and linear approximations will overestimate the function's value.

Front

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

Back

Front

What is the relationship between the rates of change of x and y in related rates problems?

Back

They are often connected through a geometric relationship, such as the Pythagorean theorem.

Front

What is the significance of the derivative in motion problems?

Back

The derivative represents the rate of change of position, which is velocity.

Front

Back

The particle is moving to the left at a speed of 4.5 units at time t = 2.

Front

Back

It indicates that the bottom of the ladder is moving away from the wall at a rate of 2 feet per second.

Front

What is the purpose of using a linear approximation centered at a point?

Back

To estimate the value of a function at a point close to the center using the slope of the tangent line.