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9.9 Using Second Derivatives

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Question 18

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

[2]

bi.

A research team models the potential energy $V$ of a chemical system as a function of its configuration $x$ using the equation

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

where $a$ and $k$ are constants and $a > 0$ .

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

[2]

bii.

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

[5]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
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.

9.9 Using Second Derivatives

Question bank

9.9 Using Second Derivatives

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 18

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

[2]

bi.

A research team models the potential energy $V$ of a chemical system as a function of its configuration $x$ using the equation

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

where $a$ and $k$ are constants and $a > 0$ .

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

[2]

bii.

[5]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
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.