The number (n) of grams of a compound forned during a certain chemical reaction is given by n=2t/(t+1) where t is time in minutes. Evaluate d^2n/dt^2 ( the rate of increase of the amount of the compound being formed) when t=4 min.
2007-01-07 13:47:39 · 4 answers · asked by babblefish186 3 in Science & Mathematics ➔ Mathematics
This is a question regarding higher order derivatives. d^2n/dt^2 basically just asks you to differentiate "n" (with respect to t) twice.
To do this, differentiate n using the quotient rule. Afterwards, just differentiate dn/dt (or n-prime) to get d^2n/dt^2.
If you have to use first principles, then use Newton's method with x_0=4
2007-01-07 13:54:19 · answer #1 · answered by Steven X 2 · 0⤊ 0⤋
n=2t/(t+1)
dn/dt = [(t+1)2 - 2t]/(t+1)^2 = 2/(t+1)^2 = 2/25 when t = 4
d^2n/dt^2 = -2(2t+2)/(t+1)^4 = -4/(t+1)^3
Substituting 4 for t, we get:
d^2n/dt^2 = -4/(4+1)^3 = -4/125 g/min
2007-01-07 22:07:09 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
This is not really a word problem, they just want you to get the second derivative with respec to t, and plug in the value t=2
2007-01-07 21:52:10 · answer #3 · answered by Anonymous · 0⤊ 0⤋
differentiate the n with respect to t twice. then evaluate the result at t=4.
2007-01-07 21:59:58 · answer #4 · answered by early_sol 2 · 0⤊ 0⤋