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9.9 Using Second Derivatives

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Question 7
a.

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

[1]
bi.

The function g(x)g(x)g(x) is defined by

g(x)=x3−4ax2+k g(x) = x^3 - 4ax^2 + k g(x)=x3−4ax2+k

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

Show that there is a stationary point where the curve crosses the yyy-axis.

[2]
bii.

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

[4]
Markscheme

9.9 Using Second Derivatives Questions

  1. A Level
  2. /Maths
  3. /9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

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