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 sometimes be a simpler …

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 the second derivative.

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 based on …

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 differentiate the …

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 of these points.

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 decreasing …