Question

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

\(14\)