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9.9 Using Second Derivatives

Easy Medium Hard

1 2 3 4

Question 4

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

[2]

bi.

The vertical displacement, $s$ , of a mechanical component is modelled by the function

s(t) = k + 15at^2 - 2t^3

where $\ge 0$ is time, and $a$ and $k$ are constants with $a > 0$ .

Show that the curve $s (t)$ has a stationary point at its $s$ -intercept.

[3]

bii.

Given that the equation $s (t) = 0$ has three distinct real roots, determine the range of possible values for $k$ in terms of $a$ . You must use the second derivative to justify the nature of the stationary points used in your calculation.

[7]

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

Easy Medium Hard

1 2 3 4

Question 4

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

[2]

bi.

The vertical displacement, $s$ , of a mechanical component is modelled by the function

s(t) = k + 15at^2 - 2t^3

where $\ge 0$ is time, and $a$ and $k$ are constants with $a > 0$ .

Show that the curve $s (t)$ has a stationary point at its $s$ -intercept.

[3]

bii.

[7]

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.