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 ...

The tangent will have an equation in the form \(y = mx + c\) so to find the equation you need to find the values of \(m\) and \(c\). First, find \(m\), the gradient of the tangent. On a diagram ...

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 ...