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For the line passing through A and B: m = (y2-y1)/(x2-x1) = (-6-4)/(7-3) = -5/2

For the perpendicular line: m = -1/(-5/2) = 2/5 

y - y1 = m*(x - x1)  >>  y - 4 = (2/5)*(x - 3)  >>...

y = (3x⁴ - 18)/x

The gradient of a tangent to a curve is equal to dy/dx 

However, we must simplify this equation before we can differentiate it;

y = 3x³ - 18/x =...

y= x³ +5x² -6x +4

dy/dx = 3x² +10x -6

...

dy/dx = 3x^2

= [4x - 1/3x³ - 3/4x⁴]¹_-2 = (4(1) - 1/3(1)³ - 3/4(1)⁴) - (4(-2) - 1/3(-2)³ - 3/4(-2)⁴) =(2 11/12) - (-8 + 8/3 - 12) ...