# Use the intermediate Value Theorem to show that x^(1/3)=1-x have at least a solution in [0,1]?

##### 1 Answer

May 25, 2018

Let be the function

This function is continous in

Now evaluate the function in extreme points

The intermediate value theorem (based on Bolzano's theorem) establish that exist a number

And this is what we want to proof. QED