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Chapter 4 | Applications of Derivatives
Figure 4.39 The function f has a local maximum at x =− 3 and a local minimum at x = 3
4.19 Consider the function f ( x ) = x 3 − ⎛ ⎝ 3 2 ⎞ ⎠ x 2 −18 x . The points c =3, −2 satisfy f ′( c ) =0. Use the second derivative test to determine whether f has a local maximum or local minimum at those points.
We have now developed the tools we need to determine where a function is increasing and decreasing, as well as acquired an understanding of the basic shape of the graph. In the next section we discuss what happens to a function as x →±∞. At that point, we have enough tools to provide accurate graphs of a large variety of functions.
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