(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)=518p35−96p+450,p>0Solve the equation E′(p)=0E'(p) = 0E′(p)=0.
Solve the equation E′′(p)=23\displaystyle E''(p) = \frac{2}{3}E′′(p)=32.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, 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.
