We can see that its minimum occurs at , i.e
We also find the same for
Conclusion follows
I have been given the triangle inequality:
||x| - |y|| <= |x + y| <= |x| + |y|
where |x| is the absolute value of x.
Now I'm supposed to prove the following:
|3x + 2| + |3x - 2| >= 4 for all real x.
Now, I tried this:
|3x + 2| + |3x - 2| >= |3x + 2 + 3x - 2| = 6|x|.
This does not solve the problem. How do I do this?