Finding Inflection Points

Front

What is an inflection point?

Back

An inflection point is a point on a curve where the sign of the curvature (the concavity) changes.

Front

How do you find inflection points?

Back

To find inflection points, determine where the second derivative of a function changes sign.

Front

Why are inflection points important in calculus?

Back

Inflection points are important because they indicate where a function changes concavity, which can provide insights into the behavior of the function.

Front

What is the second derivative test?

Back

The second derivative test is a method used in calculus to determine whether a given critical point of a function is a local maximum, local minimum, or a saddle point by analyzing the sign of the second derivative at that point.

Front

What does it mean if the second derivative is positive?

Back

If the second derivative of a function is positive at a certain point, it indicates that the function is concave up at that point, suggesting a local minimum if it's a critical point.

Front

What does it mean if the second derivative is negative?

Back

If the second derivative of a function is negative at a certain point, it indicates that the function is concave down at that point, suggesting a local maximum if it's a critical point.