**32+ Sketch The Graph Of The Derivative Of The Function Shown
Gif**. The slope of is undefined at , and the graph approaches vertical (unbounded slope) as x approaches those values. So, we actually don't have important points, but when `x` approaches 0 from the right function grows clearly they are all points of inflections because second derivative changes sign at these points.

A function of a single variable is most usefully represented by its graph. This is the same as the limit definition of the derivative at a point, but with x instead of a. This is essential as the derivative of the function will be undefined at those locations, and must be shown clearly on the graph (which is usually resolved with an open circle).

### The derivative function f is a function f' that maps each value of x to the gradient or slope of the line tangent to f(x).

F itself, f ', and f ''. This relies on a solid understanding of functions here's a video by patrickjmt showing you how to sketch a derivative given the graph of a function. Online, immediately and for free. Get this resource as part of a bundle and save up to 34%.