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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) ...
In order to do this question one has to first recognise that this is a product and thus has to be solved using Integration by parts. Firstly write out the formula: ∫u.dv/dx dx = uv - ∫v. du/dx dx ...
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