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1.10 G: Differentiation

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Question 270

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]

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

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.

Question bank