Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
For function g(x, y) = 9x² + 6y²,
the absolute minimum is 15 and the absolute maximum is 303
For given question,
We have been given a function g(x, y) = 9x² + 6y² subject to the constraint −1≤x≤1 and −1≤y≤7
We need to find the absolute maximum and minimum values of the function.
First we find the partial derivative of function g(x, y) with respect to x.
⇒ [tex]g_x=18x[/tex]
Now, we find the partial derivative of function g(x, y) with respect to x.
⇒ [tex]g_y=12y[/tex]
To find the critical point:
consider [tex]g_x=0[/tex] and [tex]g_y=0[/tex]
⇒ 18x = 0 and 12y = 0
⇒ x = 0 and y = 0
This means, the critical point of function is (0, 0)
We have been given constraints −1 ≤ x ≤ 1 and −1 ≤ y ≤7
Consider g(-1, -1)
⇒ g(-1, -1) = 9(-1)² + 6(-1)²
⇒ g(-1, -1) = 9 + 6
⇒ g(-1, -1) = 15
And g(1, 7)
⇒ g(1, 7) = 9(1)² + 6(7)²
⇒ g(1, 7) = 9 + 294
⇒ g(1, 7) = 303
Therefore, for function g(x, y) = 9x² + 6y²,
the absolute minimum is 15 and the absolute maximum is 303
Learn more about the absolute maximum and absolute minimum values of the function here:
https://brainly.com/question/16270755
#SPJ4
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
