Gradients, Tangents & Normals (Edexcel IAL Maths)

Spec point — 4.3

Gradients, tangents & normals

How do I find the gradient at a point on 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)

How do I find the equation of a tangent to a curve?

• 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 $y-f(a)=f^{'}(a)(x-a)$

How do I find the equation of a normal to a curve?

• 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 $y-f(a)=-\frac{1}{f^{'}(a)}(x-a)$

Exam Hint

• The formulae above are not in the 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).

Worked Example