CAIE A-Level Mathematics 1.7.3 Applications of Differentiation

CAIE A-Level Mathematics 1.7.3 Applications of Differentiation
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using derivatives to construct tangents and normals, test increasing or decreasing behaviour and combine rates for coordinates, arcs, areas and other changing quantities.

How this is tested

  • evaluate dy/dx at the point and use the negative reciprocal for a normal gradient
  • use the sign of a derivative throughout its domain to classify increasing or decreasing behaviour
  • apply dQ/dt = (dQ/dx)(dx/dt) and evaluate all quantities at the stated instant

Question 11(a)

[Maximum number: 3]

A curve passes through the point P(4,3) and is such that

dy dx=8x2−10(2x−3)2.\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{8}{x^{2}}-\frac{10}{(2 x-3)^{2}} .

Find the equation of the normal to the curve at P. Give your answer in the form y=m x+c.