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)=3t4−16t3The function has exactly two stationary points, at t=0t = 0t=0 and t=4t = 4t=4.
(i) Find C′′(t)C''(t)C′′(t).
(a) (ii) Determine the nature of the stationary points. Fully justify your answer.
State the range of values of ttt for which the capital C(t)C(t)C(t) is an increasing function.
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.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
