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Example Questions
Example Question #1592 : Calculus Ii
Consider the equation
.
Which of the following is equal to ?
Example Question #1593 : Calculus Ii
Define .
Give the minimum value of on the interval
.
We first look for such that
:
The two values on the interval for which this holds true are
, so we evaluate
for the values
:
The minimum value is .
Example Question #1594 : Calculus Ii
Consider the equation
.
Which of the following is equal to ?
Example Question #1 : Derivative As A Function
Define .
Give the maximum value of on the interval
.
First, we determine if there are any points at which .
The only point on the interval on which this is true is .
We test this point as well as the two endpoints, and
, by evaluating
for each of these values.
Therefore, assumes its maximum on this interval at the point
, and
.
Example Question #1591 : Calculus Ii
Consider the equation
.
Which of the following is equal to ?
Example Question #472 : Derivatives
Define .
Give the minimum value of on the interval
.
so
.
First, we find out where :
, which is on the interval.
Now we compare the values of at
:
The answer is .
Example Question #1601 : Calculus Ii
Consider the equation
.
Which of the following is equal to ?
Example Question #471 : Derivative Review
Define .
Give the minimum value of on the interval
.
Since, on the interval ,
,
.
is decreasing throughout this interval. Therefore, the minimum of
on the interval is
.
Example Question #473 : Derivatives
Consider the equation
.
Which of the following is equal to ?
Example Question #1602 : Calculus Ii
Define .
Give the minimum value of on the interval
.
Since ,
,
and is always positive. Therefore,
is an always increasing function, and the minimum value of
must be
.
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