find the average rate of change of the function f(x)=x² + 3x from x₁ = 4 to x₂ = 9. the average rate of…
find the average rate of change of the function f(x)=x² + 3x from x₁ = 4 to x₂ = 9. 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 $x_1 = 4$, then $f(x_1)=4^{2}+3\times4=16 + 12=28$.
Step3: Calculate $f(x_2)$
Given $x_2 = 9$, then $f(x_2)=9^{2}+3\times9=81+27 = 108$.
Step4: Calculate the average rate of change
Substitute into the formula: $\frac{f(x_2)-f(x_1)}{x_2 - x_1}=\frac{108 - 28}{9 - 4}=\frac{80}{5}=16$.
Answer:
16