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 \(\ds \lim_{h\to 0}\frac{f(1+h)-f(1)}{h}\) where \(\ds f(x)=\frac{3x+1}{x-2}\text{.}\) What does the result in (a) tell you about the tangent line to the graph ...

The tangent line to a graph does not exist at a corner ... Type in your polar equation and investigate the graph. Polar Curves and Cartesian Graphs 10.3 An applet showing the connection between the ...