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- How are the absolute maximum and minimum similar to and different from the local extrema?arrow_forwardFind all local maximum and minimum points of ƒ = 2x² − xy + y² − 5x + 6y – 9.arrow_forwardWe 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_forward
- 4. Find points on the straight line segment joining (-3,-1) and (3, 2) where the function f(x, y) = xy² + 1 attains its maximum value.arrow_forwardFind all points (x, y) where the functions f(x), g(x), h(x) have the same value: f (x) = 2"-5 + 3, g(x) = 2x – 5, h(x) + 10arrow_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
- Find 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 domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for which: - 3x2 (A) y (F) y s 1+ (G) y 2 * (H) y > 1+ 3x2 (Н) у >arrow_forwardConsider 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_forward
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