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>0 P(f) = f^{-10} e^{0.05f + 4}, \quad f > 0 P(f)=f−10e0.05f+4,f>0Show that the power PPP has exactly one stationary point. Fully justify your answer.
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.
