Let #r#, #s#, and #t# be the roots of the equation #x^3 - 2x + 1 = 0# in some order. What is the maximal value of #r^3 - s- t#?
Please answer!
Please answer!
1 Answer
Explanation:
This optimization problem can be solved with the contribution of the so called Lagrange Multipliers
Calling
and the restrictions
and forming the lagrangian
The stationary points are found by solving
and the solutions for maximum value are
giving the maximum as
NOTE:
This is an almost automatic procedure to obtain the maximum. A shorter way would be extracting the roots, which is easy and then making root arrangements and computing for