Question

Selected values of a continuous function f are given in the table below. What is the fewest possible number of zeros of f in the interval [0,5]?

Answer 1

Using function concepts, it is found that the fewest possible number of zeros of f in the interval [0,5] is 3.

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• When a function f(x) equals zero, that is, $f(x) = 0$, it is said that x is a zero of function.
• If in an interval the function changes it's signal, necessarily there is at least one zero on this interval.

On the table, f(x) changes it's signal three times:

• From positive to negative, between 0 and 1.
• From negative to positive, between 2 and 3.
• From positive to negative, between 3 and 4.

Thus, the fewest possible number of zeros of f in the interval [0,5] is 3.

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