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Find the average rate of change of f(x) = √x+2/x^2 -3 from x1 = 2 to x2 = 7.

Find the average rate of change of f(x) = √x+2/x^2 -3 from x1 = 2 to x2 = 7.-example-1
User Alexgibbs
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1 Answer

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The formula for the average rate of change between two points on a function is:


r=\frac{f(x_2)-f(x_1)_{}}{x_2-x_1}

Since we want between:


\begin{gathered} x_1=2 \\ x_2=7 \end{gathered}

We need to first calculate the values of the funciton in these points:


\begin{gathered} f(x_1)=f(2)=\frac{\sqrt[]{2+2}}{2^2-3}=\frac{\sqrt[]{4}}{4-3}=(2)/(1)=2 \\ f(x_2)=f(7)=\frac{\sqrt[]{7+2}}{7^2-3}=\frac{\sqrt[]{9}}{49-3}=(3)/(46) \end{gathered}

Now, we input these into the formula:


r=\frac{f(x_2)-f(x_1)_{}}{x_2-x_1}=((3)/(46)-2)/(7-2)=((3-2\cdot46)/(46))/(5)=((3-92)/(46))/(5)=((-89)/(46))/(5)=-(89)/(46)\cdot(1)/(5)=-(89)/(230)

Thus, the average rate of change is -89/230.

User Codii
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