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Differentiation

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Question 504
a.

Sketch the graph of any cubic function that has three distinct real roots and a positive coefficient of x3x^3x3.

[2]
bi.

A research team models the potential energy VVV of a chemical system as a function of its configuration xxx using the equation

V(x)=2x3−9ax2+k V(x) = 2x^3 - 9ax^2 + k V(x)=2x3−9ax2+k

where aaa and kkk are constants and a>0a > 0a>0.

Verify that the energy profile has a stationary point where it intersects the vertical VVV-axis.

[2]
bii.

Given that the equation V(x)=0V(x) = 0V(x)=0 has three distinct real roots, determine the range of possible values for kkk in terms of aaa by considering the nature and positions of the local maximum and local minimum points.

[5]
Markscheme

Differentiation Questions

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

717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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