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9.9 Using Second Derivatives

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Question 20

A model for the net capital, $C$ , of a tech startup (in millions of pounds) after $t$ years is given by

C(t) = 3t^4 - 16t^3

The function has exactly two stationary points, at $t = 0$ and $t = 4$ .

(i) Find $C^{''} (t)$ .

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

[4]

State the range of values of $t$ for which the capital $C (t)$ is an increasing function.

[2]

A revised model, $K$ , is proposed for the same startup such that

K(t) = 3t^4 + 16t^3

[3]

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 20

A model for the net capital, $C$ , of a tech startup (in millions of pounds) after $t$ years is given by

C(t) = 3t^4 - 16t^3

The function has exactly two stationary points, at $t = 0$ and $t = 4$ .

(i) Find $C^{''} (t)$ .

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

[4]

State the range of values of $t$ for which the capital $C (t)$ is an increasing function.

[2]

A revised model, $K$ , is proposed for the same startup such that

K(t) = 3t^4 + 16t^3

[3]

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.