To construct the tangent to a curve at a certain point A, you draw a line that follows the general direction of the curve at that point. An example of this can be seen below. Once the tangent is ...

Find the slopes of those tangent lines. Find the equation of those tangent lines. Find the point(s) on the curve \(y=x^3\) where the line through the point \((4,0)\) is tangent to the curve. Find ...

{10} = 20~m/s\). To find an estimate of the speed after 6.5 seconds, draw the tangent to the curve at 6.5. \(gradient = \frac{140-20}{9-4} = \frac{120}{5} = 24~m/s\) A velocity-time graph shows ...