How do we know that it is at x=0 that we get minimum potential energy; why not at x=1 or -1 where dU/dx is min.?

Question

Parikshit Ranjeet Raje · Answer

You may check the double derivative of U i.e. d 2 y/dx 2 and put the values of x. If double derivative is -ve then it is a maxima and if +ve then its a minima. V(x)= (x 4 /4) – (x 2 /2) dV/dx= x 3 - x=0 x=1,0,-1 d 2 V/dx 2 = 3x 2 -1 (double derivative) Put x=0,-1,1 d 2 V/dx 2 at x=1,-1 is +ve so minima at x=1,-1

Aishwarya Jee · Answer

But the book says the min. Potential energy is 0, obtained at X=0, is there something to do with the negative sign of (-dU/dx)=F

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How do we know that it is at x=0 that we get minimum potential energy; why not at x=1 or -1 where dU/dx is min.?

How do we know that it is at x=0 that we get minimum potential energy; why not at x=1 or -1 where dU/dx is min.?

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How do we know that it is at x=0 that we get minimum potential energy; why not at x=1 or -1 where dU/dx is min.?

How do we know that it is at x=0 that we get minimum potential energy; why not at x=1 or -1 where dU/dx is min.?

2 Answers

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