Question

I need help with this question please

Answer 1

Answer:

- $\frac{1}{12}$

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 [ a, b ] = [ - 1, 3 ] , then

f(3) = $\frac{1}{3-5}$ = - $\frac{1}{2}$

f(- 1) = $\frac{1}{-1-5}$ = - $\frac{1}{6}$

average rate of change

= $\frac{-\frac{1}{2}-(-\frac{1}{6}) }{3-(-1)}$

= $\frac{-\frac{1}{2}+\frac{1}{6} }{3+1}$

= $\frac{-\frac{1}{3} }{4}$

= - $\frac{1}{12}$

Answer 2

Answer:

Average rate of change is - 1/6 or -0.166…

Step-by-step explanation:

${ \tt{f(x) = \frac{1}{x - 5} }}$

f(-1):

${ \tt{f( - 1) = \frac{1}{( - 1 - 5)} }} \\ = { \tt{ - \frac{1}{6} }}$

f(3):

${ \tt{f(3) = \frac{1}{3 - 5} }} \\ = { \tt{ - \frac{1}{2} }}$

Average rate of change:

$= { \bf{ \frac{f(3) - f(-1)}{2} }}$

${ \tt{ = \frac{ - \frac{1}{2} - ( - \frac{1}{6} ) }{ 2 } }} \\ \\ = { \tt{ - \frac{1}{6} }}$