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Differentiation

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Question 127

A cross-section of a micro-fluidic channel is modeled by the curve with equation

3x2y−bx3+12y2=4 3x^2y - bx^3 + \frac{1}{2}y^2 = 4 3x2y−bx3+21​y2=4

where bbb is a positive constant.

a.

Show that

dydx=3x(bx−2y)3x2+y \frac{dy}{dx} = \frac{3x(bx - 2y)}{3x^2 + y} dxdy​=3x2+y3x(bx−2y)​
[4]
b.

Given that the curve has a stationary point at x=1x = 1x=1, determine the value of bbb.

[4]

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