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If and , must have a root between and ? Explain why or why not. Be sure to include sketches that support your reasoning.

First quadrant, x axis with 3 unequal tick marks labeled, from left to right, a, c, & b, y axis with 3 equal tick marks, labeled from bottom to top, f of b, m, &, f of a, horizontal line starting at (0, comma m), continuous curve starting at the point (a, comma f of A), turning up below x axis between tick marks, c & b, turning down below horizontal line, ending at the point (b, comma f of b).Intermediate Value Theorem

Let be a function continuous on the closed interval . Then for every value between and there exists a value , , such that .

Notice the condition of the Intermediate Value Theorem.