please help mean value
Two runners start a race at same time and finish in a tie.use mean value theorem to show that at some time during the race they have the same speed
(Hint:Let s1(t) be the distance function of first runner and let s2(t) be the distance function for second runner.consider f(t)=s1(t) -s2(t) )
Take the hint, then f(t) is continuous on [0,T] (where T is the time they finish),
Originally Posted by bobby77
and assume that s1 and s2 are differentiable on (0,T), then so is f and by the
mean value theorem there is some point c in (0,T) such that:
But f'(t)=s1'(t)-s2'(t), so at some point c in (0,T) s1'(c)=s2'(c) as required.