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Differentiation

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Question 543

The curve C has equation y=f(x),x>0y = f(x), x > 0y=f(x),x>0.

Given that

  • the point P(1,12)P(1, 12)P(1,12) lies on CCC
  • f′(x)=6x+kx3f'(x) = 6\sqrt{x} + \frac{k}{x^3}f′(x)=6x​+x3k​ where kkk is a constant
  • f′′(x)=0f''(x) = 0f′′(x)=0 at PPP
a.

Find the exact value of kkk.

[4]
b.

Find f(x)f(x)f(x), giving your answer in simplest form.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

649 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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