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Differentiation

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Question 610

A research team models the fuel efficiency EEE of a prototype engine as a function of its operating speed vvv (where v>0v > 0v>0). The efficiency function is determined to be convex (also known as concave up) across its entire domain. Identify which of the following functions could represent E(v)E(v)E(v).

A: E(v)=40+15ln⁡(v)E(v) = 40 + 15\ln(v)E(v)=40+15ln(v)

B: E(v)=v2+900vE(v) = \frac{v^2 + 900}{v}E(v)=vv2+900​

C: E(v)=120+2v−0.05v2E(v) = 120 + 2v - 0.05v^2E(v)=120+2v−0.05v2

D: E(v)=200(1−e−0.2v)E(v) = 200(1 - e^{-0.2v})E(v)=200(1−e−0.2v)

[3]
Markscheme

Differentiation Questions

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

717 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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