Question

A curve has the equation,
`y = 2ln(k-3x) + x^2-3x` where
`k` is a positive constant. It is also given that the curve crosses the x-axis at exactly on point. Find the value of
`k`.

Answer 1

When y=ln|x|, then x=exp(y). for y=0 (x-axis), x=1 => The curve cuts x-axis at A(1.0).

For point of minima, y’=0 => 1/|x|=0 => |x|=∞. For all x<1, y<0 (negative). Further as x→0, y→-∞. Thus the function has a global minima at x=0 => B=(0,-∞).