Current Attempt in ProgressFind the absolute extrema of the given function on the indicated closed and bounded set R.f(x, y) = xy – x – 5y; Ris the triangular region with vertices (0, 0), (0, 30), and (5, 0)Absolute maximum: iAbsolute minimum: i HintAssistance UsedA point (xo, yo) in the domain of a function f(x, y) is called a critical point of the function if f, (xo, yo) = 0 andf, (xo, Yo) = 0 orif one or both partial derivatives do not exist at (xo, yo).The Second Partials Test:Let f be a function of two variables with continuous second-order partial derivatives in some disk centered at a critical point(xo. Yo), and letD = fr (x0, Yo )fyy (xo, Yo) – f, (xo, Yo)(a) If D > 0 and f (xo, Yo) > 0, thenf has a relative maximum at (xo, Yo).(b) If D > 0 and fr (xo, Yo) < 0, thenf has a relative minimum at (xo, yo).(c) If D < 0, thenf has a saddle point at (xo, Yo).(d) If D = 0, then no conclusion can be drawn.

Calculate the value of function at all critical points. The maximum value amongall value at critical…

Find the absolute extrema of the given function on the indicated closed and bounded set R. f(x, y) = xy – x – 5y; Ris the triangular region with vertices (0, 0), (0, 30), and (5, 0) Absolute maximum: i Absolute minimum: i

Find the absolute extrema of the given function on the indicated closed and bounded set R. f(x, y) = xy – x – 5y; Ris the triangular region with vertices (0, 0), (0, 30), and (5, 0) Absolute maximum: i Absolute minimum: i

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Current Attempt in Progress
Find the absolute extrema of the given function on the indicated closed and bounded set R.
f(x, y) = xy – x – 5y; Ris the triangular region with vertices (0, 0), (0, 30), and (5, 0)
Absolute maximum: i
Absolute minimum: i

Hint
Assistance Used
A point (xo, yo) in the domain of a function f(x, y) is called a critical point of the function if f, (xo, yo) = 0 andf, (xo, Yo) = 0 or
if one or both partial derivatives do not exist at (xo, yo).
The Second Partials Test:
Let f be a function of two variables with continuous second-order partial derivatives in some disk centered at a critical point
(xo. Yo), and let
D = fr (x0, Yo )fyy (xo, Yo) – f, (xo, Yo)
(a) If D > 0 and f (xo, Yo) > 0, thenf has a relative maximum at (xo, Yo).
(b) If D > 0 and fr (xo, Yo) < 0, thenf has a relative minimum at (xo, yo).
(c) If D < 0, thenf has a saddle point at (xo, Yo).
(d) If D = 0, then no conclusion can be drawn.

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