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Differentiation

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Question 460

(Solutions based entirely on graphical or numerical methods are not acceptable.)

The operational efficiency E E\,E of a specialized power-generation turbine is modeled as a function of the internal gas pressure ppp (measured in bar), given by

E(p)=185p53−96p+450,p>0 E(p) = \frac{18}{5}p^{\frac{5}{3}} - 96p + 450, \quad p > 0 E(p)=518​p35​−96p+450,p>0
a.

Solve the equation E′(p)=0E'(p) = 0E′(p)=0.

[3]
b.

Solve the equation E′′(p)=23\displaystyle E''(p) = \frac{2}{3}E′′(p)=32​.

[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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