Question

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.)

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:

\(10\)