Question

The table below shows the function f.

Answer 1

Answer:

C

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here the closed interval is [ 3, 7 ]

f(b) = f(7) = $\frac{47}{6}$

f(a) = f(3) = $\frac{17}{2}$

f(7) - f(3) = $\frac{47}{6}$ - $\frac{17}{2}$ = - $\frac{2}{3}$

Thus

$\frac{-\frac{2}{3} }{7-3}$

= $\frac{-\frac{2}{3} }{4}$

= - $\frac{2}{3}$ × $\frac{1}{4}$ = - $\frac{1}{6}$

Average rate of change = - $\frac{1}{6}$ → C