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Differentiation

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Question 232

(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]

Differentiation Questions

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

Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions 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, matched to the Edexcel A Level Maths (9MA0) 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