How do you find the average rate of change for the function $f (x) = x^{2} + x + 3$ $f(x) = x^2+x+3$ on the indicated intervals [1,x]?

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Answer 1 · 2015-09-11T05:17:14

x+2

Rate of change would be $\frac{f (x) - f (1)}{x - 1}$ $(f(x)-f(1))/ (x-1)$

= $\frac{(x^{2} + x + 3) - 5}{x - 1}$ $((x^2+x+3) -5)/(x-1)$

= $\frac{x^{2} + x - 2}{x - 1}$ $(x^2 +x -2)/(x-1)$

= $\frac{(x + 2) (x - 1)}{x - 1} = x + 2$ $((x+2)(x-1))/(x-1)= x+2$

How do you find the average rate of change for the function f(x) = x^2+x+3f(x)=x2+x+3f(x) = x^2+x+3 on the indicated intervals [1,x]?