Question

find the average rate of change of the function from x₁ to x₂ f(x)=6x + 7 from x₁=-1 to x₂=0

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x_1\) to \(x_2\) is \(\frac{f(x_2)-f(x_1)}{x_2 - x_1}\).

Step2: Find \(f(x_1)\) and \(f(x_2)\)

Given \(f(x)=6x + 7\), \(x_1=-1\) and \(x_2 = 0\).
For \(x_1=-1\), \(f(-1)=6\times(-1)+7=-6 + 7=1\).
For \(x_2 = 0\), \(f(0)=6\times0+7=7\).

Step3: Calculate the average rate of change

Substitute into the formula: \(\frac{f(0)-f(-1)}{0-(-1)}=\frac{7 - 1}{0 + 1}\).
Since \(7-1 = 6\) and \(0+1=1\), \(\frac{6}{1}=6\).

Answer:

\(6\)