(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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
