Absolute Maximum and Minimum Values of Multivariable Function
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Why do you think that is wrong?View attachment 34355i have found the minimum of this function is (0,0) and max is (1,1) but i feel like I am doing something wrong
Please share your work!
the boundaries would be (0,0),(1,0),(1,1) and if plugged in (0,0) gives lowest value and (1,1) gives highest
i found that the critical point would be (-1,2) but it is outside the boundaries so it can not be used also i found that the boundary would be those 3 points (0,0) (1,0) and (1,1)
The boundary of the domain is not defined by three points. It is defined by three curves, namely
y = 0,
x = 1, and
y = x^2.
Graph the domain and you will see why. So, you must test all points on the boundary. Then you can be confident of your answer.
In any case, what are the minimum and maximum values in that domain?
y = 0,
x = 1, and
y = x^2.
Graph the domain and you will see why. So, you must test all points on the boundary. Then you can be confident of your answer.
In any case, what are the minimum and maximum values in that domain?
so what would the correct answer for min and max be ?
[math] z = x^2 + xy + y, \text { where } 0 \le x \le 1, \ 0 \le y \le x^2.\\ \therefore \ 0 \le x \le 1, \text { and } y = 0 \implies \min(z) = \text {WHAT, and } \max(z) = \text { WHAT?}\\ x = 0 , \text { and } y \le x^2 = 0 \implies \min(z) = \text {WHAT, and } \max(z) = \text {WHAT?}\\ 0 \le x \le 1 \text { and } 0 \le y \le x^2 \implies \min(z) = \text {WHAT, and } \max(z) = \text {WHAT?} [/math]
The answer is not a pair of ordered pairs.
Steven G
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Here is how I would do this problem. Luckily this method will work with this f(x,y).View attachment 34355i have found the minimum of this function is (0,0) and max is (1,1) but i feel like I am doing something wrong
The largest value x can be is 1
Since y<=x^2, the largest y can be is when x=1. The largest xy can be is 1*1=1.
The largest y can be is 1.
So the largest x^2 + xy + y can be is 1^2 + 1*1 + 1 = 3.
Saying that the max is (1,1) makes no sense. The max is a real number while (1,1) is a point. Maybe the max occurs at (1,1), but the max is not (1,1).