Question

If $F=2x^2-3x-2$, then select the correct statement.

• A. $x=-\frac{1}{2}$ is the position of stable equilibrium
• B. $x=2$ is the position of stable equilibrium
• C. $x=-\frac{1}{2}$ is the position of unstable equilibrium
• D. $x=2$ is the position of neutral equilibrium

Answer 1

The correct option is A $x=-\frac{1}{2}$ is the position of stable equilibrium

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

$\frac{dF}{dx}=4x-3<0$

$x<3/4$ for stable equilibrium

$x>3/4$ for unstable equilibrium

For stable $F=0$

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

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

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

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

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