We're minimizing
subject to
. Using Lagrange multipliers, we have the Lagrangian
with partial derivatives
Set each partial derivative equal to 0:
Subtracting the second equation from the first, we find
Similarly, we can determine that
and
by taking any two of the first three equations. So if
determines a critical point, then
So the smallest value for the sum of squares is
when
.
Using it's concept, the average rate of change of the function on the interval [6,13] is given by:
<h3>What is the average rate of change of a function?</h3>
The average rate of change of a function is given by the <u>change in the output divided by the change in the input</u>. Hence, over an interval [a,b], the rate is given as follows:
In this problem, we want to find the rate in the interval [6, 13], which is given as follows:
More can be learned about the average rate of change of a function at brainly.com/question/24313700
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Subtraction property of equality is used when u have 2 sides with an equal sign in the middle and u want to subtract from both sides.
Example :
2x + 3 = 7 ....subtract 3 from both sides
2x + 3 - 3 = 7 - 3
2x = 4
x = 4/2
x = 2
When subtracting real numbers..if the numbers are on the same side of the equal sign...u can just subtract on that one side
Example :
2x = 7 - 3
2x = 4
x = 4/2
x = 2
It rises to the right so the slope is negative
Slope = rise / run = 18 / -9 = -2
The y intercept is at y = -3 so using the form y = mx + b we get
y = -2x - 3 which is option B (answer)
X=-3 and y=5
2x+y=-1
-x+3y=18
3y-18=x
2(3y-18)+y=-1
6y-36+y=-1
7y=-1+36
7y=35
y=35/7
y=5
-x+3y=18
-x+3(5)=18
-x+15=18
-x=18-15
-x=3
x=-3
