The speed of a runner, in miles per hour, on a straight trail is modeled by ()2m2+9m2 - 12m) + 7, where m is the runner's distance, in miles, from the start of the trail. what is the maximum speed of the runner for 0 s m s3? (a) 6.5 (b) 6.6 (c) 7.0 (d) 7.5 15.

Option B - 6.6 miles per second

Step-by-step explanation:

Given : The speed of a runner, in miles per hour, on a straight trail is modeled by , where m is the runner's distance, in miles, from the start of the trail.

To find : What is the maximum speed of the runner for ?

Solution :

The model is given by,

Derivate w.r.t m,

For critical point put it to zero,

Derivate again w.r.t m,

At m=1,

It is minimum at m=1.

At m=2,

It is maximum at m=2.

So, the maximum speed of the runner for is given by

Therefore, the maximum speed of the runner for is 6.6 miles per second.

Option B is correct.