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Section 3.6 Sketching Graphs

One of the most obvious applications of derivatives is to help us understand the shape of the graph of a function. In this section we will use our accumulated knowledge of derivatives to identify the most important qualitative features of graphs \(y=f(x)\text{.}\) The goal of this section is to highlight features of the graph \(y=f(x)\) that are easily

  • determined from \(f(x)\) itself, and
  • deduced from \(f'(x)\text{,}\) and
  • read from \(f''(x)\text{.}\)

We will then use the ideas to sketch several examples.