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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
