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Differentiation

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Question 108

A simple model for the cost of a car journey £ C C\,C when a car is driven at a steady speed of v v\,v mph is

C=kv+v+10 C = \frac{k}{v} + v + 10 C=vk​+v+10

where k k\,k is a positive constant.

The cost of the journey is minimised when the car is driven at a steady speed of 68.0 mph.

a.

Use this model to find the value of kkk.

[5]
b.

Use d2Cdv2\displaystyle \frac{d^2C}{dv^2}dv2d2C​ to verify that C C\,C is a minimum for this value of vvv

[2]
c.

Calculate the minimum cost of the journey

[2]
Markscheme

Differentiation Questions

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

264 exam-style questions on Edexcel A Level Maths Differentiation, covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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