Sketch the graph of any cubic function that has both three distinct real roots and a negative coefficient of x3x^3x3.
The function g(x)g(x)g(x) is defined by g(x)=x3−4ax2+kg(x) = x^3 - 4ax^2 + kg(x)=x3−4ax2+k where aaa and kkk are constants and a>0a > 0a>0.
Show that there is a stationary point where the curve crosses the yyy-axis.
Given that the equation g(x)=0g(x) = 0g(x)=0 has three distinct real roots, find the range of possible values for kkk in terms of aaa by considering the positions of the local maximum and local minimum points.
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.