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

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Question 5

A potential energy function VVV is defined for all real values of xxx as

V(x)=x4+8x3 V(x) = x^4 + 8x^3 V(x)=x4+8x3

The function has exactly two stationary points, at x=0x = 0x=0 and x=−6x = -6x=−6.

a.

(i) Find V′′(x)V''(x)V′′(x).

(ii) Determine the nature of the stationary points. Fully justify your answer.

[6]
b.

State the range of values of xxx for which V(x)=x4+8x3V(x) = x^4 + 8x^3V(x)=x4+8x3 is an increasing function.

[2]
c.

A second potential function WWW is defined for all real values of xxx as

W(x)=x4−8x3 W(x) = x^4 - 8x^3 W(x)=x4−8x3

(i) State the single transformation which maps the graph of VVV onto the graph of WWW.

(ii) State the range of values of xxx for which WWW is an increasing function.

[3]
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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