Question

Find the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0,a].

Answer 1

The intermediate value theorem does not guarantee a zero for a function that is constant on an interval.

Step-by-step explanation:

The intermediate value theorem guarantees that a continuous function has a zero between two points if the function takes on values with opposite signs at those points. In this case, the function is defined as a horizontal line, which means it has a constant value along the interval [0, 20]. Since a zero cannot be found on any interval where the function is constant, there is no value of a that satisfies the condition.