Find the normal to the curve y = x^2 at x = 5.
Differentiate the original equation (y = x^2) to find the gradient (m) of the line which is a tangent to the curve.
Dy/dx = 2x
Therefore m = 2
Calculate the negative reciprocal (m2) which will give the gradient of the normal.
m2 = -0.5
Using the equation y=mx+c find the equation of the normal.
When x=5, y=25.
25=(-0.5)(5) + c
c=27.5
y=-0.5x+27.5
AS
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