Analytical Applications of Differentiation unit 5

Front

What are inflection points in the context of a function?

Back

Inflection points are points on the graph of a function where the concavity changes, which can be identified by the second derivative changing sign.

Front

How can you determine if a point is a local maximum or minimum using the first derivative?

Back

If the first derivative changes from positive to negative at a point, it is a local maximum. If it changes from negative to positive, it is a local minimum.

Front

What does the second derivative of a function indicate?

Back

Front

What is the significance of a stationary point on a graph?

Back

A stationary point is where the first derivative is zero, indicating a potential local maximum, local minimum, or a point of inflection.

Front

How do you identify increasing and decreasing intervals of a function?

Back

A function is increasing where its first derivative is positive and decreasing where its first derivative is negative.

Front

What is the relationship between the first and second derivatives in determining concavity?

Back

The first derivative indicates the slope of the function, while the second derivative indicates the concavity. A positive second derivative means the function is concave up.

Front

Back

Front

How can you use a sign chart for the first derivative to analyze a function?

Back

A sign chart for the first derivative helps determine where the function is increasing or decreasing and identifies local extrema.

Front

What is the definition of a local minimum?

Back

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

Front

What is the definition of a local maximum?

Back

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