Any point P(x, y) on a curve has a tangent line that denotes the gradient at point P. By differentiating the equation of the curve, and substituting (x, y) to the resulting equation, you would get the value of the gradient at point P.
The gradient of the tangent to a function (or curve) is denoted by .
1. Find the gradient of the tangent to the parabola at the point (1, 2).
2. Find the values of x for which the gradient of the tangent to the curve is equal to 18.
Explore tangents and normals with the Geogebra app below:
The normal is a straight line perpendicular to the tangent at the same point of contact with the curve.
If lines with gradients and are perpendicular, then
1. Find the gradient of the normal to the curve at the point where x = 4.
2. Find the equation of the normal to the curve at the point (-1, 3).