The gradient of a tangent to a curve

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Presentation transcript:

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

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

In general

Example Obtain given (i) (ii)

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)

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

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.