How do you find the average rate of change of $y = x^{2} + 7 x$ $y = x^2 + 7x$ over [1,8]?

Question

3426 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-02T17:05:06

$16$ $16$

The average rate of change is the slope on that interval.

The slope, or rise over run, measures the change in $y$ $y$ -values over the change in $x$ $x$ -values.

The $y$ $y$ -values are $f (1)$ $f(1)$ and $f (8)$ $f(8)$ and the $x$ $x$ -values are $1$ $1$ and $8$ $8$ .

Thus, the average rate of change is equal to

$\frac{f (1) - f (8)}{1 - 8}$ $(f(1)-f(8))/(1-8)$

Find $f (1)$ $f(1)$ and $f (8)$ $f(8)$ .

$f (1) = 1^{2} + 7 (1) = 8$ $f(1)=1^2+7(1)=8$

$f (8) = 8^{2} + 7 (8) = 120$ $f(8)=8^2+7(8)=120$

Thus, the average rate of change is equal to

$\frac{8 - 120}{1 - 8} = \frac{- 112}{- 7} = 16$ $(8-120)/(1-8)=(-112)/(-7)=16$

How do you find the average rate of change of y = x^2 + 7xy=x2+7xy = x^2 + 7x over [1,8]?