The volume VVV, in cubic centimetres, of a gas within a high-pressure bellows pump is modelled by the function
V(t)=4000(2t−1)3,t>0.5 V(t) = \frac{4000}{(2t - 1)^3}, \quad t > 0.5 V(t)=(2t−1)34000,t>0.5where ttt is the time in seconds.
Determine the equation of the tangent to the curve V(t)V(t)V(t) at the instant t=1.5t = 1.5t=1.5. Give your answer in the form V=mt+cV = mt + cV=mt+c.
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.
