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 = (\Delta f)/(\Delta x) = (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 = (6)/(2) = 3.`

`Answer \colon 3~\blacktriangle`