Help me on these questions please!

1. The points A (-4,-2), B (6,4) and C (4,-4) are vertices of a triangle ABC.

I found the equation of the line passing through A and B which is 3x- 5y+2=0.

The question is Point D is the midpoint of AB. Show that CD is perpendicular to AB.

2. Curve C has equation f(x) and point P (2, 10.25) lies on C.

Given that f'(x)= (x^3/2 - 2x^-3/2)^2 +2

Show that f'(x) can be written as Ax^3 + B/x^3 + D

3. x^2 +2kx-5=0

Prove that, for all real values of k, the roots of the equation are real and different.

Thanks so much in advance if you can help me.