Answer:
The maximum acceleration over that interval is 
.
Step-by-step explanation:
The acceleration of this car is modelled as a function of the variable 
.
Notice that the interval of interest 
is closed on both ends. In other words, this interval includes both endpoints: 
and 
. Over this interval, the value of 
might be maximized when is at the following:
- One of the two endpoints of this interval, where or
. - A local maximum of , where
(first derivative of 
is zero) and 
(second derivative of 
is smaller than zero.)
Start by calculating the value of at the two endpoints:
.- .
Apply the power rule to find the first and second derivatives of :
.
.
Notice that both 
and 
are first derivatives of 
over the interval .
However, among these two zeros, only 
ensures that the second derivative 
is smaller than zero (that is: 
.) If the second derivative 
is non-negative, that zero of would either be an inflection point (if
) or a local minimum (if 
.)
Therefore 
would be the only local maximum over the interval 
.
Calculate the value of at this local maximum:
.
Compare these three possible maximum values of over the interval . Apparently, would maximize the value of . That is: gives the maximum value of over the interval .
However, note that the maximum over this interval exists because 
is indeed part of the interval. For example, the same would have no maximum over the interval 
(which does not include .)
