Inequality with Max. and Min.value.

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The discussion focuses on finding the maximum and minimum values of the expression (x^3+1)(y^3+1) given the constraint x+y=1, without using calculus. Participants mention that the minimum value is straightforward to determine, while the maximum value is more complex, potentially involving a degree 5 polynomial when using calculus. There is a suggestion to share solutions for further discussion. The conversation highlights the challenge of solving the problem analytically without calculus. Overall, the thread emphasizes the mathematical exploration of inequalities under specific constraints.
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Homework Statement



If x,y\in R and x+y=1.then find max. and Min. value of (x^3+1)(y^3+1) (Without using calculus)

Homework Equations


here x+y=1 and (x^3+1)(y^3+1)


The Attempt at a Solution



I have done using Calculus...
 
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So what exactly is your problem?
The Minimum value is easy to argue.
I wonder how you found the maximum value using calculus because that involves solving a degree 5 polynomial.
You could post your answers then we can discuss a bit more.
 

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