find the average rate of change of the function ( f(x)=x^{2}+8x ) from ( x_{1}=2 ) to ( x_{2}=4 ).\nthe…

find the average rate of change of the function ( f(x)=x^{2}+8x ) from ( x_{1}=2 ) to ( x_{2}=4 ).\nthe average rate of change is (square). (simplify your answer.)

find the average rate of change of the function ( f(x)=x^{2}+8x ) from ( x_{1}=2 ) to ( x_{2}=4 ).\nthe average rate of change is (square). (simplify your answer.)

Answer

Explanation:

Step1: Calculate (f(x_1)) and (f(x_2))

For (x_1 = 2), (f(2)=2^{2}+8\times2=4 + 16=20). For (x_2 = 4), (f(4)=4^{2}+8\times4=16+32 = 48).

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)=20), (f(x_2)=48), (x_1 = 2), and (x_2 = 4) into the formula: (\frac{48 - 20}{4-2}=\frac{28}{2}).

Answer:

(14)