AP Calculus AB Unit 4 Review

Front

What is the maximum speed of a body moving along a coordinate line if its velocity graph shows a peak at 3 m/s?

Back

The body's maximum speed is 3 m/s.

Front

How do you estimate the value of a function using local linear approximation?

Back

To estimate the value of a function using local linear approximation, find the derivative at a point and use the formula: f(a) + f'(a)(x - a).

Front

What does it mean for a function to be concave up at a certain point?

Back

A function is concave up at a point if its second derivative is positive at that point, indicating that the slope of the tangent line is increasing.

Front

When is a body moving at a constant speed according to a velocity graph?

Back

A body is moving at a constant speed when the velocity graph is horizontal (slope = 0) over an interval.

Front

What is the significance of an underestimate or overestimate in local linear approximation?

Back

An underestimate occurs when the function is concave up, and an overestimate occurs when the function is concave down.

Front

How do you determine the rate at which the distance between two moving objects is changing?

Back

Use related rates by differentiating the distance formula with respect to time and applying the chain rule.

Front

What is the formula for the distance between two points moving towards or away from each other?

Back

The distance D between two points can be expressed as D = √(x² + y²), where x and y are the distances from a reference point.

Front

What is the relationship between velocity and speed?

Back

Velocity is a vector quantity that includes direction, while speed is a scalar quantity that only measures how fast an object is moving.

Front

How do you find the derivative of a function at a specific point?

Back

To find the derivative at a specific point, use the limit definition of the derivative or apply differentiation rules.

Front

What is the significance of the second derivative in determining concavity?

Back

The second derivative indicates concavity: if f''(x) > 0, the function is concave up; if f''(x) < 0, it is concave down.