- #1
The second derivative of a function is the derivative of the first derivative. It represents the rate of change of the slope of the function.
The second derivative helps us analyze the concavity of a function and identify points of inflection. It also allows us to find the maximum and minimum points of a function.
To find the second derivative, you first take the derivative of the function to get the first derivative. Then, you take the derivative of the first derivative to get the second derivative.
The second derivative is denoted as f''(x) or d²y/dx².
The second derivative tells us about the curvature of the graph of a function. A positive second derivative indicates a concave up graph, while a negative second derivative indicates a concave down graph. A zero second derivative indicates a point of inflection on the graph.