AP Calc BC Unit I

Front

What does it mean for a function's derivative to be always negative?

Back

If a function's derivative is always negative, it means that the function is decreasing for all values in its domain.

Front

What is the relationship between a function and its derivative?

Back

The derivative of a function represents the rate of change of the function. If the derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

Define critical points of a function.

Back

Critical points are values in the domain of a function where the derivative is either zero or undefined. They are potential locations for local maxima and minima.

Front

What is the Mean Value Theorem?

Back

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

Explain the concept of concavity.

Back

Concavity refers to the direction in which a curve bends. A function is concave up if its second derivative is positive, and concave down if its second derivative is negative.

Front

What is the significance of inflection points?

Back

Inflection points are points on the graph of a function where the concavity changes. They occur where the second derivative is zero or undefined.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing on an interval if its derivative is positive throughout that interval, and decreasing if its derivative is negative.

Front

What is a local maximum?

Back

A local maximum is a point in the domain of a function where the function value is greater than the values of the function at nearby points.

Front

What is a local minimum?

Back

A local minimum is a point in the domain of a function where the function value is less than the values of the function at nearby points.

Front

Define the first derivative test.

Back

The first derivative test is a method used to determine whether a critical point is a local maximum, local minimum, or neither by analyzing the sign of the derivative before and after the critical point.