find the average rate of change of the function f(x)=x^2 + 3x from x_1 = 1 to x_2 = 2. the average rate of…
find the average rate of change of the function f(x)=x^2 + 3x from x_1 = 1 to x_2 = 2. the average rate of change is . (simplify your answer.)
Answer
Explanation:
Step1: Recall the formula
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 $f(x_1)$
Given $f(x)=x^{2}+3x$ and $x_1 = 1$, then $f(x_1)=f(1)=1^{2}+3\times1=1 + 3=4$.
Step3: Calculate $f(x_2)$
Given $x_2 = 2$, then $f(x_2)=f(2)=2^{2}+3\times2=4 + 6 = 10$.
Step4: Calculate the average rate of change
Substitute into the formula: $\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{10 - 4}{2-1}=\frac{6}{1}=6$.
Answer:
6