The acoustic power PPP of a specialized sonar pulse is modeled as a function of its frequency fff (in kHz) by the equation
P(f)=f−10e0.05f+4,f>0P(f) = f^{-10} e^{0.05f + 4}, \quad f > 0P(f)=f−10e0.05f+4,f>0
Show that the power PPP has exactly one stationary point. Fully justify your answer.
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.