Front

What is the definition of the average rate of change of a function over an interval?

Back

The average rate of change of a function f(x) over the interval [a, b] is given by the formula (f(b) - f(a)) / (b - a).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does it mean for a function to be increasing at an increasing rate?

Back

A function is increasing at an increasing rate if its derivative is positive and increasing, indicating that the slope of the tangent line is getting steeper.

Tags

CCSS.HSF.IF.B.4

Front

What does it mean for a function to be decreasing at a decreasing rate?

Back

A function is decreasing at a decreasing rate if its derivative is negative but increasing, indicating that the slope of the tangent line is getting less steep.

Tags

CCSS.HSF.IF.B.4

Front

What is concavity in relation to a function's graph?

Back

Concavity refers to the direction of the curvature of a graph. A function is concave up if its second derivative is positive, and concave down if its second derivative is negative.

Front

How can you determine if a function is concave up or concave down from its graph?

Back

A function is concave up if the graph opens upwards (like a cup) and concave down if it opens downwards (like a frown).

Front

What is the significance of the first derivative of a function?

Back

The first derivative of a function indicates the rate of change of the function and helps determine where the function is increasing or decreasing.

Front

What is the significance of the second derivative of a function?

Back

The second derivative indicates the concavity of the function and can help identify points of inflection where the function changes concavity.

Front

What does it mean for a function to have a negative rate of change?

Back

A negative rate of change indicates that the function is decreasing as the input increases.

Tags

CCSS.HSF-LE.A.1B

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

How do you find the average rate of change of a piecewise function?

Back

To find the average rate of change of a piecewise function over an interval, calculate the function values at the endpoints and apply the average rate of change formula.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6