The point A with coordinates (1, 4) lies on the curve with equation y = x 3

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The point A with coordinates (1, 4) lies on the curve with equation y = x3 + 3x.

The point B also lies on the curve and has x-coordinate (1 + δx).

a. Show that the gradient of the line segment AB is given by (δx)2 + 3δx + 6.

b. Deduce the gradient of the curve at point A.

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