Question

The average rate of change of g(x) between x = 4 and x = 7 is 5/6 . Which statement must be true?

Answer 1

Answer:

$\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$  would be the correct statement.

Step-by-step explanation:

As we know that

Average rate of change = Change in output / Change in input    

                                        =  Δy  / Δx

                                        $=\frac{y_{2} -y_{1}}{x_{2} -x_{1}}$

                                        $=\frac{g(x_{2})-g(x_{1})}{x_{2}-x_{1}}$

                                         $=\frac{g(7)-g(4)}{7-4}$                    

As the average rate of change of g(x) between x = 4 and x = 7 is 5/6.

so

$\:Average\:rate\:of\:change\:=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$

                                  $\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$

Therefore, $\frac{5}{6}=\:\frac{g\left(7\right)-g\left(4\right)}{7-4}$  would be the correct statement.