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)