1st and 2nd Derivative Tests Review

Front

What is the 1st Derivative Test used for?

Back

The 1st Derivative Test is used to determine the relative maxima and minima of a function by analyzing the sign of the first derivative.

Front

What does a positive first derivative indicate about a function's behavior?

Back

A positive first derivative indicates that the function is increasing on that interval.

Front

What does a negative first derivative indicate about a function's behavior?

Back

A negative first derivative indicates that the function is decreasing on that interval.

Front

What is the 2nd Derivative Test used for?

Back

The 2nd Derivative Test is used to determine the concavity of a function and to identify points of inflection.

Front

How do you find relative extrema using the 1st Derivative Test?

Back

To find relative extrema, set the first derivative equal to zero to find critical points, then test intervals around these points to determine if the function is increasing or decreasing.

Front

What does the second derivative tell us about concavity?

Back

If the second derivative is positive, the function is concave up; if it is negative, the function is concave down.

Front

What is a point of inflection?

Back

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

Front

If f''(x) > 0 at a critical point, what can be concluded?

Back

If f''(x) > 0 at a critical point, then the function has a relative minimum at that point.

Front

If f''(x) < 0 at a critical point, what can be concluded?

Back

If f''(x) < 0 at a critical point, then the function has a relative maximum at that point.

Front

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

Back

The first derivative indicates increasing or decreasing behavior, while the second derivative indicates concavity.