Question

Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?

The pool must have been empty for the entire interval.

The pool must have been the same depth at the start of the interval as it was at the end of the interval.

The pool must have been deeper at the end of the interval than it was at the start of the interval.

The pool must have been more shallow at the end of the interval than it was at the start of the interval.

Answer 1

If D(t) gives the depth of the pool as a function of time, then the average rate of the change of the depth is given by:

\[\Large \dfrac{ D(t_{2})-D(t_{1}) }{ t_{2}-t_{1} }\]

So, what MUST be true, if that ratio = 0?