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Answer 1 · 2016-09-29T03:05:18

The average rate of change is 2.

$y = x^{2} - x + 1$ $y=x^2-x+1$

To find the average rate of change of the function in the interval $[0, 3]$ $[0,3]$ , use the formula

$A (x) = \frac{f (x) - f (a)}{x - a}$ $A(x)=frac{f(x)-f(a)}{x-a}$

$A (x) = \frac{f (3) - f (0)}{3 - 0}$ $A(x)=frac{f(3)-f(0)}{3-0}$

$A (x) = \frac{(3^{2} - 3 + 1) - (0^{2} - 0 + 1)}{3}$ $A(x)=frac{(3^2-3+1)-(0^2-0+1)}{3}$

$A (x) = \frac{7 - 1}{3}$ $A(x)=(7-1)/3$

$A (x) = \frac{6}{3} = 2$ $A(x)=6/3=2$