5. (10 points) find the average rate of change of ( f(x)=x^{2}+2x ) from ( x_{1}=3 ) to ( x_{2}=5 ).
5. (10 points) find the average rate of change of ( f(x)=x^{2}+2x ) from ( x_{1}=3 ) to ( x_{2}=5 ).
Answer
Explanation:
Step1: Calculate (f(x_1)) and (f(x_2))
Given (f(x)=x^{2}+2x), when (x_1 = 3), (f(3)=3^{2}+2\times3=9 + 6=15). When (x_2 = 5), (f(5)=5^{2}+2\times5=25+10 = 35).
Step2: Use the 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)=15), (f(x_2)=35), (x_1 = 3), (x_2 = 5) into the formula: (\frac{35 - 15}{5-3}=\frac{20}{2}).
Answer:
(10)