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 more shallow at the end of the interval than it was at the start of the 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 empty for the entire interval. the pool must have been deeper at the end of the interval than it was at the start of the interval.

Explanation:

Step1: Definir la tasa de cambio promedio

La tasa de cambio promedio \( m=\frac{f(b)-f(a)}{b - a} \), donde \( f(a) \) es el valor inicial (en el inicio del intervalo) y \( f(b) \) es el valor final (al final del intervalo).

Step2: Sustituir \( m = 0 \) en la fórmula

Si \( m = 0 \), entonces \( 0=\frac{f(b)-f(a)}{b - a} \). Multiplicando ambos lados por \( b - a \) (suponiendo \( b
eq a \)), obtenemos \( f(b)-f(a)=0 \), es decir \( f(b)=f(a) \). Esto significa que el valor de la función (en este caso, la profundidad de la piscina) en el inicio del intervalo \( a \) y al final del intervalo \( b \) es el mismo.

Answer:

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