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1.10 G: Differentiation

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Question 224

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]

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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