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. 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.
