We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into ...

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 \(({x_1,~y_1})\) ...

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 ...

This is the same as trying to find the slope of a line that only touches the curve at that point, called a tangent line. In many cases, it is impossible to find that slope using algebra alone.