Once the tangent is found you can use it to find the gradient of the graph by using the following formula: \(\text{Gradient to the curve =}~\frac {y_2-y_1} {x_2-x_1}\) where \(({x_1,~y_1})\) ...

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 ...

Find the Cartesian coordinates for the point on the curve corresponding to \(\ds \theta = \frac{\pi }{3}\text{.}\) One of graphs in Figure 4.3.1 is the graph of \(r=4\cos(3\theta)\text{.}\) Indicate ...