Mr. O. ran the Disney Marathon in 2 hours 18 minutes. Remember a marathon is 26.2 miles. Show that at least twice he had to be running at a rate of 11 miles per hour.

Determine whether Mean Value Theorem can be applied. If so, find all values x=c that satisfy the theorem, or explain why not.

Calculus AB AP

Kindly check explanation

Step-by-step explanation:

Given that:

Time taken = 2 hours 18 minutes

18 / 60 = 0.3 hours

Hence, time taken = 2.3 hours

Speed = distance / time

Speed = 26.2 / 11.3 = 11.39 mi/hr

Hence, according to the mean value theorem ;

The range of time taken is (0, 2.3) whereby a certain time, t exist when the runner attains a speed of 11.39

Since initial and final velocity is 0 ;

The runner attains a speed of 11 mi/hr between :

(0, 2.3) and (t, 2.3)

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)