Semester 1 Final Calc AB review

Front

What is concavity in calculus?

Back

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

Front

How do you determine the intervals of concavity for a function?

Back

To determine the intervals of concavity, find the second derivative of the function, set it equal to zero to find critical points, and test intervals around these points to see where the second derivative is positive or negative.

Front

What is the second derivative test for concavity?

Back

Front

Back

Front

What is the first derivative test?

Back

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

Front

What does it mean for a function to be increasing or decreasing?

Back

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

Front

How do you find the critical points of a function?

Back

Front

What is the significance of inflection points?

Back

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

Front

How do you find the intervals where a function is concave up?

Back

Front

What is the relationship between the first and second derivatives?

Back

The first derivative indicates the slope of the function (increasing or decreasing), while the second derivative indicates the concavity of the function (concave up or down).