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,
m 1x m 2 = -1
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)
y - y1= m(x - x1)
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 = 2x2 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(m 2 )of the normal is calculated from;
m 1x m 2 = -1 (where m 1 is the gradient of the tangent)
so
m 2 = - 1/( m 1)
Example
Find the equation of the normal to the curve:
y = x2 + 4x + 3, at the point (-1,0).
