Engineering Calculus Notes 336

Engineering Calculus Notes 336 - 324 CHAPTER 3 REAL-VALUED...

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Unformatted text preview: 324 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION Next, let’s find the extreme values of the same function on the unbounded set (see Figure 3.23) defined by f →∞ f −1, 1 22 = x2 + y 2 = 4 1 −2 x≤y Critical Point not in Domain f →∞ Figure 3.23: Critical Points and Boundary Behavior of f (x, y ) = x2 − 2x + y 2 on {(x, y ) | x ≤ y } x≤y: here, the lone critical point (1, 0) lies outside the set, so all the extreme behavior is “at the boundary”. There are two parts to this: first, we look at the behavior on the boundary points of S , which is the line x = y. Along this line we can write g(x) = f (x, x) = 2x2 − 2x; g′ (x) = 4x − 2 vanishes at x= 1 2 ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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