2xy + 5 - 8 + 3xy - y +7 + 3y = 5xy - 8 + 2y + 12
Answer:
a. The critcal points are at
b. Then, 
is a maximum and 
is a minimum
c. The absolute minimum is at 
and the absolute maximum is at 
Step-by-step explanation:
(a)
Remember that you need to find the points where
Therefore you have to solve this equation.
From that equation you can factor out 
and you would get
And from that you would have 
, so 
.
And you would also have 
.
You can factor that equation as 
Therefore 
.
So the critcal points are at
b.
Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since
Then, is a maximum and is a minimum
c.
The absolute minimum is at and the absolute maximum is at
Eliminate parentheses using the distributive property.
... -1 -7g +42 +6g = 36
... 41 -g = 36 . . . . collect terms
... 41 -36 = g . . . . add g-36 to both sides
... 5 = g . . . . . .. . . your answer
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
<h3>How to find the equation of a line?</h3>
The equation of a line can be represented as follows:
y = mx + b
where
Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
learn more on equation of a line here: brainly.com/question/10727767
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