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CAIE A-Level Mathematics AS 1.7.3 Differentiation Applications Questions

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

Syllabus
2028–2030
Course
Mathematics 9709
Level
AS

Exam points

  • Use the derivative at a point to find tangent and normal gradients, construct their equations, and solve related tangent or normal conditions.
  • Use the sign of the first derivative to determine where a function increases or decreases, and use first and second derivatives to locate and classify stationary points or extrema.
  • Use a specified gradient or stationary-point condition to determine an unknown coordinate or parameter.
  • Use differentiation and connected rates of change to relate variable rates at a specified instant.

CAIE A-Level Mathematics AS 1.7.3 Differentiation Applications Questions question 1

[Maximum number: 2]

The equation of a curve is y=2x2−12x+3y=2 x^{2}-\frac{1}{2 x}+3.

For positive values of x, determine whether the curve shows a function that is increasing, decreasing or neither. Give a reason for your answer.

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