1. Let f(x)= x3 + 3x2 - 1, where x is a real variable. (This is the same function that was considered in the supplementary class exercise.)
For each of the intervals on which a real zero was found in the supplementary class exercise, determine whether there is a zero on the left-hand half of the interval or on the right-hand half of the interval. (Conceiveably, the zero also could occur exactly at the midpoint ... )
Sample: Suppose you have found that there was a zero
between -3 and -2 because f(-3) < 0
and f(-2) > 0.
Then calculate f(-2.5), and
use that information (and the Intermediate Value Theorem) to determine
which of the two halves of the interval could contain the zero.
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