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Tangents

The gradient of the tangent to the curve y = f(x) at the point (x1, y1) on the curve is given by:

the value of dy/dx, when x = x1 and y = y1

Normals

Two lines of gradients m 1, m 2 respectively are perpendicular to eachother if the product,

Equation of a Tangent

The equation of a tangent is found using the equation for a straight line of gradient m, passing through the point (x1, y1)

To obtain the equation we substitute in the values for x1 and y1 and m (dy/dx) and rearrange to make y the subject.

Example

Find the equation of the tangent to the curve y = 2×2 at the point (1,2).

Equation of a Normal

The equation of a normal is found in the same way as the tangent.

The gradient(m2) of the normal is calculated from;

(where m1 is the gradient of the tangent)

so,

Example

Find the equation of the normal to the curve:

y = x2 + 4x + 3, at the point (-1,0).

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