A function fff is defined for all real values of xxx as
f(x)=x4−6x3 f(x) = x^4 - 6x^3 f(x)=x4−6x3The function has exactly two stationary points, at x=0x = 0x=0 and x=92x = \frac{9}{2}x=29.
(i) Find f′′(x)f''(x)f′′(x).
(ii) Determine the nature of the stationary points. Fully justify your answer.
State the range of values of xxx for which f(x)=x4−6x3f(x) = x^4 - 6x^3f(x)=x4−6x3 is an increasing function.
A second function ggg is defined for all real values of xxx as
g(x)=x4+6x3 g(x) = x^4 + 6x^3 g(x)=x4+6x3(i) State the single transformation which maps fff onto ggg.
(ii) State the range of values of xxx for which ggg is an increasing function.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
