A curve CCC has equation y=2x3−15x+kx,x>0y = 2x^3 - 15x + \frac{k}{x}, \quad x > 0y=2x3−15x+xk,x>0 where kkk is a constant. The point PPP with xxx-coordinate 111 lies on CCC. Given that PPP is a stationary point of CCC:
show that k=−9k = -9k=−9.
Determine the nature of the stationary point at PPP, justifying your answer.
The curve CCC has a second stationary point.
Using algebra, find the xxx-coordinate of this second stationary point.
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.