1. The gradient of a tangent to a curve
Calculus .
The gradient of a tangent to a curve
The gradient of a tangent to a curve is given by the notation
Given y as a function of x.
Then The gradient of the tangent to the curve will be given by

2. Example
Obtain the derivative for each of the following
(i)
(ii)
(iii)

3. In general

4. Example
Obtain given
(i)
(ii)

5. Example
Given
Obtain an expression for
Find the gradient of the curve at the point (2, 9)
Hence find the equation of the tangent at the point (2, 9)

6. The sketch is of the graph Find an expression for
Example
The sketch is of the graph
Find an expression for
Find the coordinates at the point where the gradient is zero
Hence write down the equation of the line of symmetry for the parabola. x y

7. A Level Past Paper Question
Find the equation of the tangent to the curve at the point x = 1, and find where this tangent meets the line y = x.