Question

What is the average rate of change of f(x) from x1=-10 to x2=-3? Please write your answer rounded to the nearest hundredth. f(x)= the square root of -9x+5

Answer 1

The average rate of change of f(x) from x1=-10 to x2=-3 is approximately -0.57.

Step-by-step explanation:

To find the average rate of change of f(x) from x1=-10 to x2=-3, we can use the formula:

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

Plug in the values:

Average Rate of Change = (sqrt(-9(-3)+5) - sqrt(-9(-10)+5)) / (-3 - (-10))

Simplify the equation:

Average Rate of Change = (sqrt(27+5) - sqrt(90+5)) / (-3 + 10)

Average Rate of Change = (sqrt(32) - sqrt(95)) / 7

Use a calculator to find the values of the square roots:

Average Rate of Change = (5.65 - 9.75) / 7

Average Rate of Change = -0.5714

Rounding to the nearest hundredth, the average rate of change of f(x) from x1=-10 to x2=-3 is approximately -0.57.

Answer 2

We have the following information

`\begin{gathered} x_1=-10 \\ x_2=-3 \end{gathered}`

and the function

`f(x)=\sqrt[]{-9x+5}`

In order to find the average rate, we need to find y1 and y2. Then, by substituting x1 into the function, we have

`\begin{gathered} f(-10)=\sqrt[]{-9(-10)+5} \\ f(-10)=\sqrt[]{90+5} \\ f(-10)=\sqrt[]{95} \end{gathered}`

Similarly, by substituting x2, we get

`\begin{gathered} f(-3)=\sqrt[]{-9(-3)+5} \\ f(-3)=\sqrt[]{27+5} \\ f(-3)=\sqrt[]{32} \end{gathered}`

Therefore, the average rate is given by

`(f(x_2)-f(x_1))/(x_2-x_1)=\frac{\sqrt[]{32}-\sqrt[]{95}}{-3-(-10)}`

which gives

`\begin{gathered} (f(x_2)-f(x_1))/(x_2-x_1)=\frac{\sqrt[]{32}-\sqrt[]{95}}{7} \\ (f(x_2)-f(x_1))/(x_2-x_1)=(5.6568-9.7467)/(7) \\ (f(x_2)-f(x_1))/(x_2-x_1)=-(4.0899)/(7) \end{gathered}`

Therefore, the average rate is

`(f(x_2)-f(x_1))/(x_2-x_1)=-0.58`