Mean Value Theorem
Supposing that f(x) is a continuous function that satisfies the conditions below:
0. f(x) ,is continuous in [a,b]
,
1. f(x) ,is differentiable in (a,b)
Then there exists a number c, s.t. a < c < b and
[tex]f\mleft(b\mright)-f\left(a\right)=f‘\left(c\right)b-a[/tex]
However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.
As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.
Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).
