Let
f(x)=5 ·x2+2 ·x−3 and let x0= 1.
The average rate of change of f between x= 1 and x= 1.18 equals ?
I assume your function is
$\displaystyle f(x) = 5x^2 + 2x - 3$.
You have $\displaystyle f(1) = 5(1)^2 + 2(1) - 3$
$\displaystyle = 5 + 2 - 3$
$\displaystyle = 4$
Also $\displaystyle f(1.18) = 5(1.18)^2 + 2(1.18) - 3$
$\displaystyle = 6.962 + 2.36 - 3$
$\displaystyle = 6.322$.
The average rate of change will be given by
$\displaystyle \frac{f(1.18) - f(1)}{1.18 - 1}$
$\displaystyle = \frac{6.322 - 4}{0.18}$
$\displaystyle = \frac{2.322}{0.18}$
$\displaystyle = 12.9$.