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 .

### Examples:

1. Find the gradient of the tangent to the parabola at the point (1, 2).

### Show Answer

So the gradient of the tangent at (1, 2) is 2.

2. Find the values of *x* for which the gradient of the tangent to the curve is equal to 18.

### Show Answer

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

### Examples:

1. Find the gradient of the normal to the curve at the point where *x* = 4.

### Show Answer

So the gradient of the normal is

2. Find the equation of the normal to the curve at the point (-1, 3).

### Show Answer