Using the derivative to find the gradient of a curve
To find the gradient of a curve y= f(x) at any point on the curve, substitute the x‑coordinate of the point into the derivative f'(x)
Using the derivative to find a tangent
At any point on a curve, the tangent is the line that goes through the point and has the same gradient as the curve at that point
For the curve y = f(x), you can find the equation of the tangent at the point (a, f(a)) using
Using the derivative to find a normal
At any point on a curve, the normal is the line that goes through the point and is perpendicular to the tangent at that point
For the curve y = f(x), you can find the equation of the normal at the point (a, f(a)) using
The formulae above are not in the Edexcel exam formulae booklet, but if you understand what tangents and normals are, then the formulae follow from the equation of a straight line combined with parallel and perpendicular gradients (see Worked Example below).
Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.