Potential energy function along `x-`axis in a certain force field is given as
`U(x)=(x^(4))/(4)-2x^(3)+(11)/(2)x^(2)-6x`
For the given force field `:-`
(i)the points of equilibrium are `x=1`, `x=2` and `x=3`
(ii) the point `x=2` is a point of unstable equilibrium.
(iii) the points `x=1` and `x=3` are points of stable equilibrium.
(iv) there exists no point of neutral equilibrium.
The correct option is `:-`

Options

A. (a) `(i),(ii),(iv)`
B. (b) `(i),(ii),(iii),(iv)`
C. (c) (iii),(iv)
D. (d) (ii),(iii)

Answer

B

Explanation

For equilibrium
points,
`F=-(dU)/(dx)=0rArrx^(3)-6x^(2)+11x-6=0rArrx=`
`1,x=2` and `x=3`
In stable equilibrium , `(d^(2)U)/(dx)gt0rArrx=1` and `x=3` are stable while `x=2` is unstable.
In neutral equilibrium, `(dU)/(dx)=0` and `(d^(2)U)/(dx)=0`