A patient suffering from manflu is admitted to the Centre for Tropical Diseases, and his white blood cells are monitored before and after the administration of treatment. During the first eight hours, it is found that the number of white blood cells, in thousands per unit of blood, can be modelled by the equation:
y=x^2-4x+12

find the minimum number of white blood cells during the first four hours

Question

A patient suffering from manflu is admitted to the Centre for Tropical Diseases, and his white blood cells are monitored before and after the administration of treatment. During the first eight hours, it is found that the number of white blood cells, in thousands per unit of blood, can be modelled by the equation:
y=x^2-4x+12 

find the minimum number of white blood cells during the first four hours

anonymous · Answer

x is the time in hours after admission and y is the white blood cell count

jack1 · Answer

8,000

jack1 · Answer

i think...

jack1 · Answer

$y = x^2 - 4x + 12$
$y' = 2x - 4$
when y' = 0... parabola at minimum (in this case... maximum in others)
$y' = 2x - 4$
$0 = 2x - 4$
$4 = 2x $
$2 = x $

so minimum occurs at time = 2hrs

sub that back into main equation
$y = x^2 - 4x + 12$
$y = (2)^2 - 4(2) + 12$
$y = 4 - 8 + 12$
$y = 8$

jack1 · Answer

y = blood cell count in thousands... so 8000