The first derivative test provides an analytical tool for finding local extrema, but the second derivative can also be used to locate extreme values. Using the second derivative can …

We dive into the fascinating realm of second derivatives, starting with the function y=6/x². Together, we apply the power rule to find the first derivative, then repeat the process to reveal …

A derivative basically gives you the slope of a function at any point. The derivative of 2x is 2. Read more about derivatives if you don't...

Jun 6, 2025 · This lesson explains the visual links among f f, f ′ f ′, and f ′ ′ f ′′, shows how to sketch a derivative function graph from a curve, and demonstrates how to find the second derivative …

Jan 26, 2024 · To find the second derivative of a function, we simply differentiate the function in the usual way, and then we take the result and differentiate it again. In other words, we …

In the following table, we evaluate the second derivative at each of the critical points and use the second derivative test to determine whether f f has a local maximum or local minimum at any …

The second derivative tells whether the curve is concave up or concave down at that point. If the second derivative is positive at a point, the graph is bending upwards at that point.

Jan 2, 2024 · Use this applet to visualize the relations among a function, its first derivative function and its second derivative function.

This page explore the use of the first and second derivative to graph functions.

A differentiable function is concave up whenever its first derivative is increasing (equivalently, whenever its second derivative is positive), and concave down whenever its first derivative is …