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Pearson Edexcel IAL Mathematics P1.4.3 Tangents, normals & gradients

Practise using derivatives to find tangent and normal gradients, equations of lines, and constants fixed by points on a curve.

Syllabus
First assessment 2019
Course
Mathematics YMA01
Level
AS

Exam points

  • calculate f'(a) at a point, then form a tangent equation in y=mx+c
  • use the negative reciprocal gradient to write a normal through a given point
  • link a given tangent gradient to f'(x) to solve for constants

P1.4.3 - Tangents, normals and gradients question 1

[Maximum number: 3]

The curve C has equation y=f(x) where x>0

Given that
- f′(x)=(x+3)2xx\mathrm{f}^{\prime}(x)=\frac{(x+3)^{2}}{x \sqrt{x}}
- the point P(4,20) lies on C

Hence find the equation of the tangent to C at P, giving your answer in the form
ax+by+c=0 where a, b and c are integers to be found.

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