Derivatives

Front

What is a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable. It is a measure of how a function's output value changes as its input value changes.

Front

How do you find the derivative of a polynomial function?

Back

Front

What does it mean for a function to have a horizontal tangent line?

Back

A function has a horizontal tangent line at a point where its derivative is zero, indicating a potential local maximum or minimum.

Front

What is the power rule for derivatives?

Back

Front

What is the significance of a negative derivative?

Back

A negative derivative indicates that the function is decreasing at that point.

Front

What is the first derivative test?

Back

The first derivative test is used to determine the local maxima and minima of a function by analyzing the sign of the derivative before and after a critical point.

Front

How do you find critical points of a function?

Back

Front

What does it mean if the derivative changes from positive to negative?

Back

If the derivative changes from positive to negative at a point, the function has a local maximum at that point.

Front

What is the second derivative?

Back

The second derivative is the derivative of the derivative. It provides information about the concavity of the function and can indicate points of inflection.

Front

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

Back

To find the slope of a function at a specific point, evaluate the derivative at that point.