The only statement that is true regarding the given graph of polynomial b(x) is; Option D; Over the interval [0, 1], b(x) is negative and is decreasing.
The given graph represents the polynomial b(x). Let us look at the options;
Option A; Over the interval (0, 1), we can see that the curve is decreasing from b(x) = 0 to b(x) = -2. Thus, the statement is wrong.
Option B; Over the interval of (0, 1), b(x) is not positive over the interval (0, 1) and so the statement is wrong.
Option C; Over the interval of (0, 1), b(x) is not positive and increasing and so the statement is wrong.
Option D; Over the interval of (0, 1), b(x) is negative and is also decreasing and so this option is correct.
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