A curve CCC has equation
y=2x3−15x+kx,x>0 y = 2x^3 - 15x + \frac{k}{x}, \quad x > 0 y=2x3−15x+xk,x>0where 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 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.
