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Extremal value problems - easy
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Problem №1
Find the minimal value of the function
for
.
Solution:
The minimal value could be in both ends of the interval or in a point, in which there is a local minimum for the function. We calculate
and
, which is obviously not the minimal value.
All that is left is to find the local extrema of the function.
, so there are extrema in
and
.
, so it is not a minimal value.
. So the minimal value is
and is reached in two points -
and
.
Problem №2
Find the maximum value of the function
if
x
is a number between
-5
and
13
.
Solution:
Since
f(x)
is a linear function whose slope is
1
, a positive number, it is strictly increasing for all
x
. Therefore its maximal value is reached for the largest value of
x
,
x=13
and
f(x)=13-5=8
.
Problem №3
Find the maximal value for the function
Solution:
It is known that
. We multiply this by 4 and get
, so the maximal value for this function is 4.
Problem №4
Find the minimal value for the function
.
Solution:
, we add
-1
to both sides of the inequality and get
.
Submit a problem here.
Problem text:
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