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Differentiation

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Question 230

A specialist optical lens has a cross-section defined by the curve CCC. The coordinates (x,y)(x, y)(x,y), measured in millimeters, of the surface of the lens satisfy the equation

x2y+10y=2x3−15x2+k,y>0 x^2 y + 10y = 2x^3 - 15x^2 + k, \quad y > 0 x2y+10y=2x3−15x2+k,y>0

where kkk is a constant.

a.

Find dydx\dfrac{dy}{dx}dxdy​ in terms of xxx and yyy.

[3]
b.

The point P(p,3)P(p, 3)P(p,3), where ppp is a constant, lies on CCC. Given that PPP is the minimum turning point on CCC,

find

(i) the value of ppp

(ii) the value of kkk

[5]

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank