Average rate of change? How would I figure the following problem out?


  Find the average rate of change of $g(x)=x^2+3x+7$ from $x=5$ to $x=9$


My thought is that I would plug in 5 and 9 for the x values to get the y values. And the use the slope formula $\frac{y_2-y_1}{x_2-x_1}$.
Yes, your solution is correct.

Differentiating first is a detour.
The good thing here is that you have a quadratic equation, so differentiating w.r.t. $x$ , you get a linear equation...which makes it easy to find average rate of change.

Consider your equation $$g(x)=x^2+3x+7$$
differentiate it w.r.t. $x$ $$g'(x)=2x+3$$

The naive way of doing this question is finding $g'(5), g'(6),g'(7), g'(8),g'(9)$ and then finding its average. Alternatively, just find the average of $g'(5)$ and $g'(9)$. You will get 17.