Let f(x, y) = xy² be defined the on triangle with vertices (0, 0), (0, 3) and (1,0). We want to find the absolute minimum and maximum values that f attains on this triangle. One part of the process is to find the points on the hypotenuse where f may assume an extreme value. Let (x, y) be a point on the hypotenuse. Write the value f(x, y) as a function of x. f(x, y) = x(x + 3)² f(x, y) = 9x(x³ - 2x + 1) 9x3³ +54x+81 9x(x + 1)²
Let f(x, y) = xy² be defined the on triangle with vertices (0, 0), (0, 3) and (1,0). We want to find the absolute minimum and maximum values that f attains on this triangle. One part of the process is to find the points on the hypotenuse where f may assume an extreme value. Let (x, y) be a point on the hypotenuse. Write the value f(x, y) as a function of x. f(x, y) = x(x + 3)² f(x, y) = 9x(x³ - 2x + 1) 9x3³ +54x+81 9x(x + 1)²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let f(x, y) = xy² be defined the on triangle with vertices
(0, 0), (0, 3) and (1,0).
We want to find the absolute minimum and maximum values that f attains on this
triangle.
One part of the process is to find the points on the hypotenuse where f may
assume an extreme value.
Let (x, y) be a point on the hypotenuse. Write the value f(x, y) as a function of
x.
f(x, y) = x(x + 3)²
f(x, y) = 9x(x³ - 2x + 1)
9x³ +54x+81
9x(x + 1)²
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