How do you find the average rate of change of f(x)=x^3-3x+5 over [5,7]?

Oct 19, 2015

Just plug the values $5 \mathmr{and} 7$ in the function and see what $y$ does.

Explanation:

$f \left(7\right) = {7}^{3} - 3 \cdot 7 + 5 = 327$
$f \left(5\right) = {5}^{3} - 3 \cdot 5 + 5 = 115$

Then you divide difference in $f \left(x\right)$ by difference in $x$:

$\frac{\Delta f \left(x\right)}{\Delta x} = \frac{327 - 115}{7 - 5} = \frac{212}{2} = 106$