Final answer:
Zeros of a function are where it crosses the x-axis. The function is specified as positive before x=-1 and after x=2, which suggests it crosses the x-axis at x=-1 and x=2, making these points zeros. Zeros at infinity are not possible, and without more information, we cannot definitively establish x=6 as a zero.
Step-by-step explanation:
You mentioned a function is positive over the intervals (x | -∞ < x < -1) and (x | 2 < x < 6). These are the intervals where the function values are above the x-axis. Zeros of a function, also known as roots or x-intercepts, occur at the values of x where the function crosses or touches the x-axis. Since the function is positive (above the x-axis) before x=-1 and after x=2, it must cross the x-axis at these points to change sign. Therefore, the zeros of the function are likely to be x = -1 and x = 2, because it cannot have zeros where the function is exclusively positive or negative. Zeros do not occur at infinity, and the other endpoint, x=6, is not necessarily a zero unless the function turns negative after x=6.
Based on this reasoning, the most probable answer to your question is option c): Zeros at (x = -1) and (x = 6). However, since the function is not specified as negative between x=2 and x=6, the zero at x=6 is not definitively established. If indeed the function remains positive till x=6 and only then transitions to negative, then x=6 would be a zero as well. Without more information about the behavior of the function between the intervals given, we cannot be certain of this endpoint.