Page 58 - Calc for the Clueless

Possible inflection points: y" = 0. Using the quadratic formula and then substituting these values into the
original, we get approximately (2.34,4.86) and (-0.34,9.23). These are both inflection points. Test for cusps:
-
+
|f'(0)| is infinite, f(0) = 0. f'(0 ) is negative and f'(0 ) is positive. Cusp points down. Left-end and right-end
2/3
substitution: f(-1) = 25 (-1,25), f(5) = 5 . The point is approximately (5,2.92).
Whew!!!! Let us sketch:

Other Aids

Symmetry:

1. f(x) = f(-x). Symmetrical about the y axis.

2. f(x) = -f(-x). Symmetrical about the origin.

3. g(y) = g(-y). Symmetrical about the x axis. This is only found in graphing curves that are not functions of x.

Example 31—

y axis symmetry

Example 32—

Symmetric origin