Find the Maximum Value/ Chapter 3 Polynomial and Rational Functions

Question

Suppose x+y-=(Square root of 2). Find the maximum value of x^2+y^2. Hint x^2+y^2=(x+y)^2 - 2xy

Answer 1

W = (x+y)^2 - 2xy

W = 2 - 2xy

 

but x + y = √2

 

if x is a very large positive number then y will be a very large negative number.

 

-2xy will be -(+)(-) therefore positive. thereby making W ever larger as x gets larger.

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W = 2 - 2xy   substitute y = √2 - x

W = 2 - 2x( √2 - x )

W = 2 - 2√2x + 2x^2

rearranged into standard notation

W = 2x^2 - 2√2x + 2

 

which looks like a normal, open-up parabola that tends to infinity as x gets very large or very small.