Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where 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 = 3x3 - 18x-1
dy/dx = 3(3x2) - (-1)(18x-2)
= 9x2 + 18x-2 = 9x2 + 18/x2
When x = 3,
dy/dx = 9(9) + 18/9 = 83
RO
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