Potential energy function along \( \mathrm{x} \)-axis in a certain force field is given as \[ U(...

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Potential energy function along \( \mathrm{x} \)-axis in a certain force field is given as
\[
U(x)=\frac{x^{4}}{4}-2 x^{3}+\frac{11}{2} x^{2}-6 x .
\]
P
W
For the given force field :-
(i) the points of equilibrium are \( x=1, x=2 \) and \( x=3 \).
(ii) the point \( \mathrm{x}=2 \) 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 :-
(1) (i), (ii), (iv)
(2) (i), (ii), (iii), (iv)
(3) (iii), (iv)
(4) (ii), (iii)
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