Answer:
14.29% probability that Marlon's friend will think of the number 9
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
There are 7 numbers from 5 to 11(5,6,7,8,9,10,11)
9 is one of them
So
14.29% probability that Marlon's friend will think of the number 9
Rolle's Theorem states that:
If f is a continuous function in [a,b] and is differentiable in (a,b)
such that f(a)=f(b)
Then there exist a constant c in between a and b i.e. c∈[a,b]
such that: f'(c)=0
Here we have the function f(x) as:
where x∈[-1,3]
Also,
f(-1)=15
(Since,
)
and f(3)=15
( Since,
)
Hence, there will exist a c∈[-1,3] such that f'(c)=0
Hence, the c that satisfy the conclusion is: c=1