Inequality with Max. and Min.value.

[man111]

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...

 

[betel]

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.