Question

Can you help me please I just paid 100 dollar for the tutor version and I can’t find one tutor

Answer 1

The Solution.

Given the function below:

$f(x)=\frac{1}{x+9}\text{ and the interval \lbrack{}10,10+h\rbrack}$

The average rate of change in the given interval is

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

In this case,

$a=10,b=10+h$

So,

$f(a)=f(10)=\frac{1}{10+9}=\frac{1}{19}$$f(b)=f(10+h)=\frac{1}{10+h+9}=\frac{1}{19+h}$

Substituting in the formula, we have

$\text{Average rate of change =}\frac{\frac{1}{19+h}-\frac{1}{19}}{10+h-10}$$\begin{gathered} \text{Average rate of change =}\frac{\frac{19-(19+h)}{19(19+h)}}{h}=\frac{-h}{19h(19+h)}=\frac{-1}{19(19+h)} \\ \end{gathered}$

So, the correct answer is

$\frac{-1}{19(19+h)}$