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Problem: Supposte

x \in[-5,-3]

and

y \in[2,4]

. What is the largest possible ...

Mar 29, 2024

Problem: Supposte

x \in[-5,-3]

and

y \in[2,4]

. What is the largest possible value of

\frac{x+y}{x-y} ?

Generated Graph

Solution by Steps

step 1

To find the largest possible value of the function

f(x, y) = \frac{x+y}{x-y}

, we need to consider the behavior of the function over the domain

x \in [-5, -3]

and

y \in [2, 4]

step 2

The asksia-ll calculator has determined that there is no global maximum for the function within the given domain

step 3

However, we can analyze the function's behavior at the boundaries of the domain to find the maximum value within the given intervals

step 4

At the boundaries, the function

f(x, y)

will take the form of

\frac{-5+y}{-5-y}

\frac{-3+y}{-3-y}

\frac{x+2}{x-2}

, and

\frac{x+4}{x-4}

for the respective edges of the domain

step 5

By evaluating these expressions at the endpoints of the intervals for

x

and

y

, we can find the maximum value of

f(x, y)

within the domain

Answer

The asksia-ll calculator did not find a global maximum, but the maximum value can be approximated by evaluating the function at the boundaries of the domain.

Key Concept

Boundary Analysis of a Function

Explanation

When a function does not have a global maximum within a closed interval, the maximum value can sometimes be found by evaluating the function at the boundaries of the domain.