Question

What is the average rate of change of the function f(x) = x^2 – 2x + 4 over the interval –2 ≤ x ≤ 3?

Answer 1

The rate of change of a function is the increase or decrease that a function experiences as the independent variable changes from one value to another.

The corresponding equation of the average rate of change is:

`TVM(x_1,x_2)=(f(x_2)-f(x_1))/(x_2-x_1)`

In this case, x1 is 3 and x2 is 3

Remember that according to the notation of the limits, they take the values of 2 and 3.

Now, we solve f(3) and f(2)

`\begin{gathered} f(3)=3^2-2\cdot(3)+4 \\ f(3)=9-6+4 \\ f(3)=7 \end{gathered}`
`\begin{gathered} f(2)=2^2+2\cdot(2)+4 \\ f(2)=4-4+4 \\ f(2)=4 \end{gathered}`

This way now we can replace the values in the TVM equation and I will solve this.

`\begin{gathered} TVM(3,2)=\frac{7-4}{3-1_{}} \\ TVM(3,2)=(3)/(1)=3 \end{gathered}`

In conclusion, the average rate of change of the function