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−2rwhere 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 Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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.
