A potential energy function VVV is defined for all real values of xxx as
V(x)=x4+8x3V(x) = x^4 + 8x^3V(x)=x4+8x3
The function has exactly two stationary points, at x=0x = 0x=0 and x=−6x = -6x=−6.
(i) Find V′′(x)V''(x)V′′(x).
(ii) Determine the nature of the stationary points. Fully justify your answer.
State the range of values of xxx for which V(x)=x4+8x3V(x) = x^4 + 8x^3V(x)=x4+8x3 is an increasing function.
A second potential function WWW is defined for all real values of xxx as
W(x)=x4−8x3W(x) = x^4 - 8x^3W(x)=x4−8x3
(i) State the single transformation which maps the graph of VVV onto the graph of WWW.
(ii) State the range of values of xxx for which WWW is an increasing function.
Practise Edexcel A Level Maths 9.9 Using Second Derivatives with exam-style questions for A Level Maths. 57 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.