Question

What is the average rate of change from 0 to 2 of f(x)=x^3-x+4​

Answer 1

$\mathbf{Task.} ~ \mathrm{What~is~the~average~rate~of~change~from~0~to~2~of~} f(x) = x^{3} - x + 4?$

$\mathrm{The~average~rate~} \upsilon ~ \mathrm{of~change~of~the~function~} f(x) ~ \mathrm{over~the~interval~} [x_{1}; \ x_{2}]\\\mathrm{can~be ~ found~on~the~formula \colon}$

$\boxed{\upsilon = \dfrac{\Delta f}{\Delta x} = \dfrac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}} }$

$\mathrm{For~the~function,} ~ f(x) = x^{3} - x + 4 ~ \mathrm{the~average~rate~of~change~over~the~interval}\\\mathrm{from~0~to~2 \colon}$

$f(0) = 0^{3} -0 + 4 = 4;$

$f(2) = 2^{3} - 2 + 4 = 8 + 2 = 10;$

$\Delta f = 10 - 4 = 6;$

$\Delta x = 2 - 0 = 2.$

$\upsilon = \dfrac{6}{2} = 3.$

$Answer \colon 3~\blacktriangle$