Question

For the function f(x)=2x² + 5x + 3, find the average rate of change of f from x=2 to x = 3.

Answer 1

We have a function f(x) for which we have to find the average rate of change from x = 2 to x = 3.

The function f(x) is defined as:f

$f(x)=2x^2+5x+3$

The average rate of change (r) for a function in a interval [a, b] can be expressed as:

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

In this case, b = 3 and a = 2, we can calculate the average rate of change as:

$\begin{gathered} r=\frac{f(3)-f(2)}{3-2} \\ \\ r=\frac{2(3)^2+5(3)+3-(2(2)^2+5(2)+3)}{1} \\ \\ r=2(9)+15+3-2(4)-10-3 \\ r=18+15-8-10 \\ r=15 \end{gathered}$

Answer: the average rate of change of f(x) from x = 2 to x =3 is 15.