find the average rate of change of the function f(x)=x^2 + 3x from x_1 = 2 to x_2 = 4. the average rate of…
find the average rate of change of the function f(x)=x^2 + 3x from x_1 = 2 to x_2 = 4. the average rate of change is . (simplify your answer.)
Answer
Explanation:
Step1: Find f(x1)
Substitute (x_1 = 2) into (f(x)=x^{2}+3x). [f(2)=2^{2}+3\times2=4 + 6=10]
Step2: Find f(x2)
Substitute (x_2 = 4) into (f(x)=x^{2}+3x). [f(4)=4^{2}+3\times4=16+12 = 28]
Step3: Calculate average rate of change
The formula for the average rate of change of a function from (x_1) to (x_2) is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). [ \begin{align*} \frac{f(4)-f(2)}{4 - 2}&=\frac{28-10}{4 - 2}\ &=\frac{18}{2}\ &=9 \end{align*} ]
Answer:
9