If the lines x + y = a and x – y = b touch the
curve y = x² – 3x + 2 at the points where the curve intersects the x-axis, then $${a \over b}$$ is equal to _______.

Let ƒ(x) be a polynomial of degree 3 such that ƒ(–1) = 10, ƒ(1) = –6, ƒ(x) has a critical point at x = –1 and ƒ'(x) has a critical point at x = 1. Then ƒ(x) has a local minima at x = _______.

Let the normal at a point P on the curve
y² – 3x² + y + 10 = 0 intersect the y-axis at $$\left( {0,{3 \over 2}} \right)$$ .
If m is the slope of the tangent at P to the curve, then |m| is equal to