Given points pı = , and p3 in R², P2 let S = conv{pj,P2»P3}. For each linear functional f, find the maximum value m of f on the set S, and find all points x in S at which f(x) = m. a. f(x1,x2) = x1 + x2 b. f(x1,x2) = X1 – X2 c. f(x1,x2) =-2x1 + x2

Find 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).

Given two points A(1, 8) and B(6, 14). Find the point C on the x-axis so that the total distance AC + BC is a Minimum Distance. {Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.} Give at least 3 decimal places. Minimum Total Distance of occurs when C = ,0) DO NOT USE CALCULUS.

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