Question

what is the average rate of change of the equation f(x)=x^2+3x-5 from x=2 to x=4

Answer 1

The formula to calculate the average rate of change is as follows:

$R=\frac{f(b)-f(a)}{b-a}$

Where "a" represents the starting point and "b" the ending point.

So, a = 2 and b = 4 in this case, so we have:

$\begin{gathered} a=2 \\ f(a)=f(2)=2^2+3\cdot2-5=4+6-5=5 \\ b=4 \\ f(b)=f(4)=4^2+3\cdot4-5=16+12-5=23 \end{gathered}$

Thus:

$R=\frac{23-5}{4-2}=\frac{18}{2}=9$

The average rate of change is 9.