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3.6 Differentiation (A-level only)

3.6 Differentiation (A-level only)

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Question 148

A function fff is defined for all real values of xxx as

f(x)=x4−6x3 f(x) = x^4 - 6x^3 f(x)=x4−6x3

The function has exactly two stationary points, at x=0x = 0x=0 and x=92x = \frac{9}{2}x=29​.

a.

(i) Find f′′(x)f''(x)f′′(x).

(ii) Determine the nature of the stationary points. Fully justify your answer.

[6]
b.

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.

[2]
c.

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.

[3]
Markscheme

3.6 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6 Differentiation (A-level only)

333 exam-style questions on WJEC A Level Maths 3.6 Differentiation (A-level only), covering 3.6.1 Differentiation (A-level only), 3.6.2 Differentiation (A-level only), 3.6.3 Differentiation (A-level only), 3.6.4 Differentiation (A-level only), 3.6.5 Differentiation (A-level only), 3.6.6 Differentiation (A-level only), 3.6.7 Differentiation (A-level only), and 3.6 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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