Let's put all of our differentiation abilities to use, by analyzing the graphs of various functions. As you will see, the derivative and the second derivative of a function can tell us a lot about the function's graph.
Critical points are points where a function may obtain their minimum or maximum value. They play a critical role (pun intended) in analyzing the increasing and decreasing intervals of functions, and in finding their minimum and maximum points.
Concavity describes the shape of a graph as it increases or decreases: a graph that's concave up is shaped like a cup, U, and a graph that's concave down is shaped like a cap, ∩. Learn more about concavity and how it relates to a function's second derivative.