[tex]\mathbf{Task.} ~ \mathrm{What~is~the~average~rate~of~change~from~0~to~2~of~} f(x) = x^{3} - x + 4?[/tex]
[tex]\mathrm{The~average~rate~} \upsilon ~ \mathrm{of~change~of~the~function~} f(x) ~ \mathrm{over~the~interval~} [x_{1}; \ x_{2}]\\\mathrm{can~be ~ found~on~the~formula \colon}[/tex]
[tex]\boxed{\upsilon = \dfrac{\Delta f}{\Delta x} = \dfrac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}} }[/tex]
[tex]\mathrm{For~the~function,} ~ f(x) = x^{3} - x + 4 ~ \mathrm{the~average~rate~of~change~over~the~interval}\\\mathrm{from~0~to~2 \colon}[/tex]
[tex]f(0) = 0^{3} -0 + 4 = 4;[/tex]
[tex]f(2) = 2^{3} - 2 + 4 = 8 + 2 = 10;[/tex]
[tex]\Delta f = 10 - 4 = 6;[/tex]
[tex]\Delta x = 2 - 0 = 2.[/tex]
[tex]\upsilon = \dfrac{6}{2} = 3.[/tex]
[tex]Answer \colon 3~\blacktriangle[/tex]
