watch the video and then solve the problem given below. click here to watch the video. find the average rate…

watch the video and then solve the problem given below. click here to watch the video. find the average rate of change of the function ( f(x)=x^{2}+7x ) from ( x_{1}=1 ) to ( x_{2}=2 ). the average rate of change is ( square ). (simplify your answer.)

watch the video and then solve the problem given below. click here to watch the video. find the average rate of change of the function ( f(x)=x^{2}+7x ) from ( x_{1}=1 ) to ( x_{2}=2 ). the average rate of change is ( square ). (simplify your answer.)

Answer

Explanation:

Step1: Recall the formula for average rate of change

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: Calculate (f(x_1)) and (f(x_2))

Given (f(x)=x^{2}+7x), when (x_1 = 1), (f(1)=1^{2}+7\times1=1 + 7=8). When (x_2=2), (f(2)=2^{2}+7\times2=4 + 14 = 18).

Step3: Substitute into the formula

(\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{18 - 8}{2-1}). Since (18−8 = 10) and (2 - 1=1), then (\frac{18 - 8}{2-1}=\frac{10}{1}=10).

Answer:

(10)