Page 55 - Calc for the Clueless

x = -3 is not in the domain.

y intercept: x = 0 (0,9). Possible max, min: y' = 0 x = 0. We get the point (0,9). (0,9) is a maximum since y" is
always negative. No inflection point since y" is never equal to 0.

Since the domain is finite, we must get values for the left and right ends of x = -1, y = 8 (-1,8). x = 4, y = -7 (4,-
7). We see that (4,-7) is an absolute minimum, (-1,8) is a relative minimum, and (0,9) is an absolute maximum.

We will examine several examples with fractional exponents. We might get cusps or a second kind of inflection
point.

Given y = f(x)

1. |f'(c)| = infinity.

2. f(c) exists [f(c) is some number].

3. A. f'(c ) is negative and f'(c ) is positive, and the cusp looks like this:
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B. f'(c ) is positive and f'(c ) is negative, and the cusp looks like this:

As we will see, if f'(c ) and f'(c ) have the same sign, we will get another kind of inflection point.
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Example 27—