Teste 2ª Derivada (máx/mín)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
classificação
About this calculator
The second derivative test calculator is a useful tool to verify if a function has a maximum or minimum at a specific point. This is done by calculating the second derivative of the function and checking if it is positive or negative at the point in question.
The second derivative of a function indicates the rate of change of the first derivative. If the second derivative is positive, it indicates that the function is increasing and, therefore, the point is a minimum. If the second derivative is negative, it indicates that the function is decreasing and, therefore, the point is a maximum.
Here, you can enter the function and the point at which you want to verify the existence of a maximum or minimum. The calculator will automatically calculate the second derivative and inform you whether the point is a maximum or minimum.
Frequently asked questions
How do the calculations work?
The calculations are performed automatically by the calculator, based on the classification formula of maxima and minima. You only need to enter the function and the point at which you want to verify the existence of a maximum or minimum.
What are the conditions for a point to be a maximum or minimum?
A point is a maximum if the second derivative of the function is negative at the point in question, and a minimum if the second derivative is positive.
Can I use the calculator with trigonometric functions?
Yes, the calculator can be used with trigonometric functions. Just enter the trigonometric function and the point at which you want to verify the existence of a maximum or minimum.
What happens if the second derivative is equal to zero?
If the second derivative is equal to zero, the calculator cannot determine if the point is a maximum or minimum. In that case, additional methods must be used to determine the nature of the point.