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Differentiation

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Question 90

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

C(t)=3t4−16t3 C(t) = 3t^4 - 16t^3 C(t)=3t4−16t3

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

a.

(i) Find C′′(t)C''(t)C′′(t).

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

[4]
b.

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

[2]
c.

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

K(t)=3t4+16t3 K(t) = 3t^4 + 16t^3 K(t)=3t4+16t3

(c) (i) State the single transformation which maps the graph of CCC onto the graph of KKK.

(c) (ii) State the range of values of ttt for which KKK is an increasing function.

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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