As a tangent is a straight line it is described by an equation in the form \(y - b = m(x - a)\). You need both a point and the gradient to find its equation. You are usually given the point - it's ...

Transformations of Functions 1.3 An applet illustrating how transformations affect the graph of a function. Transformations are represented both algebraically and graphically. Construction of the ...

An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.

To find an estimate of the speed after 6.5 seconds, draw the tangent to the curve at 6.5. \(\text{Gradient} = \frac{140 - 20}{9 - 4} = \frac{120}{5} = 24 \:\text{m/s}\) A velocity-time graph shows ...