Chapter 16, Problem 4P

The specific growth rate of a yeast that produces an antibiotic is a function of the food concentration c,

$g=\frac{2c}{4+0.8c+c^2+0.2c^3}$

As depicted in Fig. P16.4, growth goes to zero at very low concentrations due to food limitation. It also goes to zero at high concentrations due to toxicity effects. Find the value of c at which growth is a maximum.

FIGURE P16.4

The specific growth rate of a yeast that produces an antibiotic versus the food concentration.