Semester 1 Final Calc AB review

Front

What is the definition of a relative maximum in calculus?

Back

A relative maximum is a point in the domain of a function where the function value is greater than the values of the function at nearby points.

Front

What is the definition of a relative minimum in calculus?

Back

A relative minimum is a point in the domain of a function where the function value is less than the values of the function at nearby points.

Front

How do you find relative extrema of a function?

Back

To find relative extrema, take the derivative of the function, set it to zero to find critical points, and use the second derivative test or the first derivative test to determine if they are maxima or minima.

Front

What is the second derivative test?

Back

The second derivative test is a method to determine the concavity of a function at a critical point. If the second derivative is positive, the function is concave up (local minimum); if negative, it is concave down (local maximum).

Front

What is a point of inflection?

Back

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

Front

What does it mean for a function to be concave up?

Back

A function is concave up on an interval if its second derivative is positive on that interval, indicating that the graph of the function is curving upwards.

Front

What does it mean for a function to be concave down?

Back

A function is concave down on an interval if its second derivative is negative on that interval, indicating that the graph of the function is curving downwards.

Front

Back

Relative maximum at x = 1 and relative minimum at x = 2.

Front

How do you determine the concavity of a function?

Back

To determine the concavity of a function, compute the second derivative. If the second derivative is positive, the function is concave up; if negative, it is concave down.

Front

What is the first derivative test?

Back

The first derivative test is used to determine whether a critical point is a local maximum or minimum by analyzing the sign of the first derivative before and after the critical point.