(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.
