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1.9.17 Concavity and the second derivative (A-level only)

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Question 6
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

1.9.17 Concavity and the second derivative (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9.17 Concavity and the second derivative (A-level only)

57 exam-style questions on OCR (MEI) A Level Maths 1.9.17 Concavity and the second derivative (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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