2nd Derivative Test

Front

What does the second derivative test determine about a function at a critical point?

Back

It helps to determine whether the critical point is a local maximum, local minimum, or neither.

Front

If f''(a) < 0, what can be concluded about the point (a, f(a))?

Back

It is a local maximum.

Front

If f''(a) > 0, what can be concluded about the point (a, f(a))?

Back

It is a local minimum.

Front

What is a point of inflection?

Back

A point where the concavity of the function changes, which occurs when f''(x) = 0.

Front

How do you find the points of inflection for a function?

Back

Set the second derivative f''(x) equal to zero and solve for x.

Front

What does it mean if f''(x) = 0 at a point?

Back

It indicates a potential point of inflection, but further testing is needed to confirm.

Front

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

Back

The second derivative indicates the concavity of the function: f''(x) > 0 means concave up, f''(x) < 0 means concave down.

Front

What is the significance of a local maximum in terms of the first and second derivatives?

Back

At a local maximum, f'(x) = 0 and f''(x) < 0.

Front

What is the significance of a local minimum in terms of the first and second derivatives?

Back

At a local minimum, f'(x) = 0 and f''(x) > 0.

Front

Back