The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula P=[150t^2]-1800t+6300, where t is the time in months from its introduction, find the time until the minimum price is reached.
2007-04-10 15:29:02 · 4 answers · asked by Nicky 2 in Science & Mathematics ➔ Mathematics
I dont speak english very well, but i'll try to help you
you have to take derivative to the formula and then make it equal to zero
P = 150t^2 -1800t+6300
Taking derivative
P' = 2*150t - 1800
P' = 300t - 1800
Making it equal to zero
300t - 1800 = 0
t = 1800/300
t = 6 months this is the answer
I hope i help you
2007-04-10 15:38:05 · answer #1 · answered by zindagii_peru 4 · 0⤊ 0⤋
I haven't done this for a bit but im pretty sure you have a calculus problem here where you need to use the derivative to find the critical #'s.... lets see if i can do this a sec
the derivative would be P' = 300t -1800
critical numbers: 0= 300t -1800
1800= 300t
t= 6
find out if critical number is a minimum or a maximum...
300(5) -1800 = -300 slope decreases first
300(7) -1800 = 300 slope increases second
t=6 is a minimum
therefore it will take 6 months to reach the minimum price
2007-04-10 15:39:18 · answer #2 · answered by Joel D 1 · 0⤊ 0⤋
just differentiate the given equation and equate the resultant equation to 0.
so 300t-1800 = 0
or t = 6 seconds. ans
2007-04-10 15:35:39 · answer #3 · answered by Anks 1 · 0⤊ 0⤋
dP/dt= 300t-1800 =0 t=6 month
2007-04-10 15:37:31 · answer #4 · answered by santmann2002 7 · 0⤊ 0⤋