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- Consider the function F (x, y) = x2 + 2y. Among the set of points (x, y) satisfying the equation x2 + y2 = 6y, find all the points at which the minimum and maximum values of F(x,y) subject to this constraint, and find the minimum and maximum values.arrow_forwardFind the stationary points and determine if each stationary point gives a local maximum or local minimum or neither. i. f(x1, X2, X3) = x + 2x3 + x + x1X2- 2x3- 7x1 + 12 ii. f(x1, X2, X3) = 2x1 - xỉ + 10x2 - x + 3x3 - x3arrow_forwardFind the maximum and minimum values of the function f(x, y) = 2x² + 3y² - 4x-5 on the domain 2 + y² 256. The maximum value of f(x,y) is: List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7). The minimum value of f(x, y) is: List points where the function attains its minimum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7).arrow_forward
- We know that f(x, y, z)= x³- 9x² + y² + z² +24x-4z +20. Determine the optimum value of the function f(x, y, z) and state that the optimum value is the maximum or minimum value.arrow_forwardB=16arrow_forwardExamine 2x² - 4xy+3y² - 8x+8y-1=0 for maximum and minimum points. Max. at (-3,-1): Min. at (3, 5) Max. at (5. 3): Min. at (-1, -3) Max. at (-1, -3): Min. at (5.3) O Max. at (3. 5): Min. at (-3,-1)arrow_forward
- Geometrically represent the setA = {(x, y) ∈ R²| x ≥ 0 e x² + y² ≤ 4}Determine if the function constraintf(x, y) = x² + 2y² + 2x set A has absolute maximum and minimum points. If these points exist, find them.arrow_forward1) is it a convex function or a concave function? Explain 'why' in terms of the given equation. 2) does local minimum exist? yes/no?arrow_forwardfind a so that f (x) = ax2 + 8x -8 has a minimum value of -24arrow_forward
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