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Differentiation

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Question 215

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. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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