function analysis online practice complete this assessment to review what youve learned. it will not count…

function analysis online practice complete this assessment to review what youve learned. it will not count toward your grade. which statement about the average rate of change over the interval a, b for the function f(x) is true? (1 point) the average rate of change is negative if f(b) < f(a). the average rate of change can be calculated using the formula (b - a)/(f(b)-f(a)). the average rate of change cannot be zero. the average rate of change can be calculated using the formula (f(b)-f(a))/(a - b).

function analysis online practice complete this assessment to review what youve learned. it will not count toward your grade. which statement about the average rate of change over the interval a, b for the function f(x) is true? (1 point) the average rate of change is negative if f(b) < f(a). the average rate of change can be calculated using the formula (b - a)/(f(b)-f(a)). the average rate of change cannot be zero. the average rate of change can be calculated using the formula (f(b)-f(a))/(a - b).

Answer

Explanation:

Step1: Record la fórmula de tasa de cambio promedio

La tasa de cambio promedio de una función $f(x)$ en el intervalo $[a,b]$ está dada por $\frac{f(b)-f(a)}{b - a}$.

Step2: Analizar cada opción

  • Si $f(b)<f(a)$, entonces $f(b)-f(a)<0$ y $b - a>0$ (ya que $b>a$ para un intervalo $[a,b]$), así que $\frac{f(b)-f(a)}{b - a}<0$. La primera opción es verdadera.
  • La fórmula correcta es $\frac{f(b)-f(a)}{b - a}$, no $\frac{b - a}{f(b)-f(a)}$, así que la segunda opción es falsa.
  • Si $f(b)=f(a)$, la tasa de cambio promedio es $\frac{f(b)-f(a)}{b - a}=0$, así que la tercera opción es falsa.
  • La fórmula correcta es $\frac{f(b)-f(a)}{b - a}$, no $\frac{f(b)-f(a)}{a - b}$, así que la cuarta opción es falsa.

Answer:

The average rate of change is negative if $f(b)<f(a)$.