In this video we are going to take a look at how derivative information gets incorporated into graphs of a function and its first and second derivative. So, if we are given a graph f(x) we will look how to construct a shape of graph of a f and graph of a f. This is a sort of pretending that we do not have formula for f. So the point is to understand how the three graphs are related one to another. On the first slide we will see some ideas that we will be using through this lecture and then we will do some examples.
vertically lining up the plots of
- this allows you to more easily incorporate information from one
graph into another graph.
based on the graph of
mark locations of horizontal tangents in
Positive slopes in
correspond to positive values in
negative slopes in
correspond to negative values in
information to sketch the graph by filling things in between the
you already have marked.
Graphs of f, f', f''
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