If point A had co-ordinates (2,11) and I wanted to find the equation of the tangent of the curve of x² + 3x + 1, and then the equation of the normal, would I do it like this?:
dy/dx = 2x + 3
Sub co-ordinate of x: 2
Gradient of tangent = 7
y-y1 = m(x-x1)
y-11 = 7(x-2)
y-11 = 7x-14
y = 7x-3
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Gradient of normal [m1 x m2 = -1] 7 x -1 = -1/7
y -11 / x - 2 = -1/7
= 7y + x - 79 = 0