Dave wants to build a rectangular screened-in porch that is 20 feet long, and it will extend 6 feet out from the backside of his
1 answer:
You might be interested in
You can use the properties of logarithm to get to the solution.
The approximate value for given term is given by
When you raise a number with an exponent, there comes a result.
Lets say you get
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
Some properties of logarithm are:
Thus,
The approximate value for given term is given by
Learn more about logarithm here:
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
.)