The potential energy VVV, in Joules, of a particle in a localized field is modelled by the function V(r)=(2r−5)4e−2rV(r) = (2r - 5)^4 e^{-2r}V(r)=(2r−5)4e−2r, where r r\,r is the distance from a fixed origin in centimeters.
Show that the rate of change of potential energy with respect to distance is given by dVdr=K(2r−5)3(9−2r)e−2r\frac{dV}{dr} = K(2r - 5)^3(9 - 2r)e^{-2r}drdV=K(2r−5)3(9−2r)e−2r where K K\,K is a constant to be determined.
Hence find the exact coordinates of the two stationary points of the function V(r)V(r)V(r).
A second particle's potential energy is modelled by the function W(r)W(r)W(r), where W(r)=3V(r−2)W(r) = 3V(r - 2)W(r)=3V(r−2) Determine the coordinates of the maximum stationary point for the function W(r)W(r)W(r).
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.