If F = 2x^2 -3x -2 , then choose correct option

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5.Work, Energy, Power and Collision

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If $F = 2x^2 -3x -2$, then choose correct option

A

$x = -1/2$ is position of stable equilibrium

B

$x = 2$ is position of stable equilibrium

C

$x = -1/2$ is position of unstable equilibrium

D

$x = 2$ is position of neutral equilibrium

Solution

$F=2 x^{2}-3 x-2$

$\frac{d F}{d x}=4 x-3<0$

$x<3 / 4$ for stable equilibrium

$x>3 / 4$ for unstable equilibrium

For stable $F=0$

$2 x^{2}-3 x-2=0$

$2 x^{2}-4 x+x-2=0$

$2 x(x-2)+1(x-2)=0$

$(2 x+1)(x-2)=0$

$x=-\frac{1}{2},$

Standard 11

Physics

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