Second Derivative Test FAQs

What is Second Derivative Test for Minimum and Maximum?

Second derivative test is used to find the maxima and minima of any function if the second derivative is negative at a point then it gives the maxima of the function and if it is positive at any point then it gives the minima.

What is the difference between second and first derivative test?

The difference in first and second derivative test lies in the fact that first derivative test only provides us with critical points and does not tell if it is a point of local maximum or local minimum whereas second derivative test tells us if the point is a local maximum or local minimum.

What are the applications of second derivative test?

Applications of second derivative test are as follows: It can also help us to determine the extremities of the curve. It can also help us to know about the orientation of a parabola.

What is a point of Inflection?

A point is said to be point of inflection where the concavity of the curve either changes from concave up to concave down or concave down to concave up.

What is the condition for second derivative test for local Maxima?

For any function f(x) at point x = k, if f”(k) < 0 where f'(k) is either 0 or not defined, then function is said to have local maxima at x = k, and f'(k) is the local maximum value.

What is the condition for second derivative test for local Minima?

For any function f(x) at point x = k, if f”(k) > 0 where f'(k) is either 0 or not defined, then function is said to have local minima at x = k, and f'(k) is the local minimum value.

What do you mean by critical point?

The point at which the first derivative of a function is zero or does not exist is called the critical point.

What is the nature of graph of the function at the point of local maximum?

At the point of local maximum, the graph of the function is concave downward.

What is the nature of graph of the function at the point of local minimum?

At the point of local minimum, the the graph of the function is concave upward.

Second Derivative Test is one of the methods in calculus to find the maxima and minima of a curve. Other than, the second derivative test there is also a first derivative, which can be referred to as a rudimentary version of the second derivative test.

First derivative test helps us find critical points for a given function but does not tell us about the nature of the function at these points. We also come across cases where we cannot get critical points as the first derivative test fails. Second derivative test is used in these cases. The second derivative test clearly tells us if the critical point obtained is a point of local maximum or local minimum. Second derivative test is also helpful in solving various problems in different fields such as science, physics, and engineering. In this article, we shall discuss the second derivative test in detail.