find the average rate of change of the function f(x)=x² + 9x from x₁ = 5 to x₂ = 6. the average rate of…
find the average rate of change of the function f(x)=x² + 9x from x₁ = 5 to x₂ = 6. the average rate of change is □. (simplify your answer.)
Answer
Explanation:
Step1: Calculate f(x1)
Given (f(x)=x^{2}+9x), when (x_1 = 5), (f(x_1)=5^{2}+9\times5=25 + 45=70)
Step2: Calculate f(x2)
When (x_2 = 6), (f(x_2)=6^{2}+9\times6=36+54 = 90)
Step3: Use average - rate - of - change formula
The average rate of change formula is (\frac{f(x_2)-f(x_1)}{x_2 - x_1}). Substitute (f(x_1)=70), (f(x_2)=90), (x_1 = 5) and (x_2 = 6) into the formula: (\frac{90 - 70}{6 - 5}=\frac{20}{1}=20)
Answer:
20