Respuesta :
Answer:
0 < t < [tex]\frac{5}{3}[/tex]
After 1.67 days the stocks would be sold out.
Step-by-step explanation:
The price of a certain computer stock after t days is modeled by
p(t) = 100 + 20t - 6t²
Now we will take the derivative of the given function and equate it to zero to find the critical points,
p'(t) = 20 - 12t = 0
t = [tex]\frac{20}{12}[/tex]
t = [tex]\frac{5}{3}[/tex] days
Therefore, there are two intervals in which the given function is defined
(0, [tex]\frac{5}{3}[/tex]) and ([tex]\frac{5}{3}[/tex], ∞)
For the interval (0, [tex]\frac{5}{3}[/tex]),
p'(1) = 20 - 12(1) = 20
For the interval ([tex]\frac{5}{3}[/tex], ∞),
p'(2) = 20 - 12(2) = -4
Positive value of p'(t) in the interval (0, [tex]\frac{5}{3}[/tex]) indicates that the function is increasing.
0 < t < [tex]\frac{5}{3}[/tex]
Since at the point t = 1.67 days curve is showing the maximum, so the stocks should be sold after 1.67 days.
