The output signal RRR, measured in millivolts, of a high-precision sensor is modeled by the function
R(t)=12tln(4t)t>0R(t) = 12\sqrt{t} \ln(4t) \quad t > 0R(t)=12tln(4t)t>0
where 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 Edexcel A Level Maths 9.4 The Product Rule with exam-style questions for A Level Maths. 30 questions, matched to the Edexcel A Level Maths (9MA0) 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.