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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 219

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]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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