The population of a colony of bacteria is modeled by the function , for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical into the colony's environment. At which time(s) is the bacteria population growing at an instantaneous rate of 0, going from positive growth just prior, to negative growth right after?
(Points : 1)
x = 0.39382
x = 0.58746
x = 1.71842
x = 2.23498
x = 0.39382 and x = 2.23498

Question

The population of a colony of bacteria is modeled by the function ,  for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical into the colony's environment. At which time(s) is the bacteria population growing at an instantaneous rate of 0, going from positive growth just prior, to negative growth right after?
(Points : 1)
       x = 0.39382
       x = 0.58746
       x = 1.71842
       x = 2.23498
       x = 0.39382 and x = 2.23498

anonymous · Answer

the function is given in the screenshot, this is one of the two Im stuck on

ranga · Answer

The rate of growth is dP/dx.  Set it to 0 and solve for x.  That is when the instantaneous rate of growth is 0.Going from positive to negative means it is a maxima.