Page 56 - Calc for the Clueless

We will test for the cusp first or second kind of inflection point.

1. f'(2)= infinity

2. f(2) = 3 (2,3)

+
-
3. f'(2 ) is negative, f'(2 ) is positive. Cusp with the point down.
4/5
1/5
x intercept: y = 0.-3 = (x - 2) . (x - 2) = ±(-3) , which is imaginary. No x intercepts, y intercept: x = 0. y =
1/4
4/5
4/5
(-2) + 3. [0,(-2) + 3] = A. No round max or min and no inflection points, f(1000) is positive and f(-1000) is
positive. Both ends go to plus infinity. The sketch:

Example 28—

Intercept (0,0). No round max or min and no inflection points.

1. |f'(0)| = infinity

2. f(0) = 0

-
+
3. f'(0 ), f'(0 ) both positive. Second kind of inflection point.
4. f(100,000) positive and f(-100,000) negative. The right end goes to plus infinity and the left end goes to
minus infinity.

The sketch:

Instructors have been known to give messy examples. While I know yours would never give one, here are two
that will take time.

Example 29—