Answer:<em> 10 miles</em>
Step-by-step explanation:
<em>Mile 1: 3.00</em>
<em>Mile 2: 3.50</em>
<em>Mile 3: 4.00</em>
<em>Mile 4: 4.50</em>
<em>Mile 5: 5.00</em>
<em>Mile 6: 5.50</em>
<em>Mile 7: 6.00</em>
<em>Mile 8: 6.50</em>
<em>Mile 9: 7.00</em>
<em>Mile 10: 7.50</em>
The slope of f(x) is 10 and the slope of g(x) is 5; g(x) has the greater y-intercept.
To find the slope of f(x), we use the slope formula: m=(y₂-y₁)/(x₂-x₁) = (-1--11)/(0--1) = (-1+11)/(0+1) = 10/1 = 10.
To find the slope of g(x), we just look at the form it is in. It is written in slope-intercept form, y=mx+b, where m is the slope. The number in g(x) that would correspond to m is 5.
The y-intercept of f(x) is found by looking at the points. Any y-intercept will have an x-coordinate of 0; the only point like this in the table is (0, -1) so the y-intercept is -1.
For g(x), we again look at the form y=mx+b. The number that corresponds with b is the y-intercept; in this case, it is 1. 1>-1, so g(x) has the larger y-intercept.
, you have
, the derivative is
