When the curve crosses the \(x-axis\) the value of \(y = 0\).

If \(y = 0\) then \( 0= x^2 +3x +2 \)

\(x_1 = \frac{-3+\sqrt{9-4(2)}}{2} = -1\)

\(x_2 = \frac{-3-\sqrt{9-4(2)}}{2} = -2\)

\( y = (x+1)(x+2)\)

\(\frac{dy}{dx} = (x+1) +(x+2)\)

At \(x_1 = -1\)

\(\frac{dy}{dx} = 0+1 = 1\)

At \(x_1 = -2\)

\(\frac{dy}{dx} =-1+0 = -1\)

Thus the slope of the curve at \((-1,0) \) is 1 and -1 at \((-2,0) \)