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Example 2 (Continued): Sketching a Parabola

Sketch the parabola y = -½x2. The first two derivatives are

05_limits_g_approx-268.gif

The only critical point is at x = 0. The table of values follows.

x

y

dy/dx

d2y/dx2

Comments

limx→-∞

-∞

vertical

x = 0

0

0

-1

max, ∩

limx→∞

-∞

-∞

vertical

The parabola is drawn in Figure 5.4.9, using Steps 1-5.

 

05_limits_g_approx-269.gif

Figure 5.4.9


Last Update: 2006-11-15