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 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.
