The output signal RRR, measured in millivolts, of a high-precision sensor is modeled by the function
R(t)=12tln(4t)t>0 R(t) = 12\sqrt{t} \ln(4t) \quad t > 0 R(t)=12tln(4t)t>0where ttt is the time in milliseconds after the sensor is triggered. The signal is zero at time TTT.
State the value of TTT.
The signal reaches its minimum value at the point MMM.
Use calculus to find the exact coordinates of MMM.
Hence find the range of the function S(t)S(t)S(t) where
S(t)=−5R(t) S(t) = -5R(t) S(t)=−5R(t)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.
