Unit 5 AB Flashcard Bellwork

Front

What is the average rate of change of a function f(x) over an interval [a,b]?

Back

The average rate of change of a function f(x) over an interval [a,b] is calculated as (f(b) - f(a)) / (b - a).

Front

Define critical points of a function.

Back

Critical points of a function are values of x where the derivative f'(x) is either zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

What are the conditions for Rolle's Theorem to apply?

Back

Rolle's Theorem applies if: 1) f is continuous on [a,b], 2) f is differentiable on (a,b), and 3) f(a) = f(b).

Front

What does it mean if g'(-2)=0 for a function g(x)?

Back

If g'(-2)=0, it indicates that x=-2 is a critical point of the function g(x).

Front

What is the definition of an inflection point?

Back

An inflection point is a point on the curve of a function where the concavity changes, which can be identified where the second derivative is zero or undefined.

Front

Explain the significance of a relative maximum.

Back

A relative maximum is a point where the function value is higher than the values of the function at nearby points, indicating a peak in the graph.

Front

What is the difference between a relative maximum and a relative minimum?

Back

A relative maximum is a peak point where the function value is higher than surrounding values, while a relative minimum is a valley point where the function value is lower than surrounding values.

Front

What is the first derivative test?

Back

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

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Front

What is the definition of differentiability?

Back

A function is differentiable at a point if it has a defined derivative at that point, meaning the function has a tangent line at that point.