(optimization problem) Find the number between 0 and 1 for which the difference between the cube roof of that number and the number itself is greatest.

Question

mr.math · Answer

Let's construct the problem first. We're asked to maximize $x^{\frac{1}{3}}-x$, where $0\le x\le 1$.

mr.math · Answer

Define $f(x)=x^{\frac{1}{3}}-x$ on [0,1]. f has its extreme values either on a critical point or on the boundaries. You should start by finding f' and its zeros. Evaluate f(x) at these zeros and at the boundary points (0 and 1). The maximum of these is your optimal.

anonymous · Answer

Thank you :)

mr.math · Answer

If something is unclear, don't hesitate to ask :)

anonymous · Answer

Sure. Thanks again.

mr.math · Answer

You're welcome!