The problem involves finding a positive number that minimizes the expression x² + (1/x²). Participants are exploring calculus concepts related to optimization and critical points.
Participants are engaged in verifying the correctness of the solution and exploring the implications of the critical point found. There is a focus on confirming whether the identified point is indeed a minimum and if other values could potentially yield a smaller result.
There is an emphasis on the requirement for the solution to be a positive number, and some participants are considering the implications of the function's concavity in relation to the minimum value.
yoyo16 said:Is it possible for the minimum to be a smaller value or would the smallest value be 1?
yoyo16 said:Homework Statement
Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.
Homework Equations
The Attempt at a Solution
y=X^2+(1/X^2)
Derivative=2x-2x^(-3)
0=2x-2x^3
2/x^3=2x
2=2x^4
1=x^4
x=1
The answer I got was 1 but I'm not sure if this is right. Can someone please tell me if I did it right or wrong. If wrong, can you point out my mistake. Thanks :)