If f(x) is an exponential decay curve then the derivative of f(x) is increasing and negative.
Is this correct?
If not what's the answer?
2006-10-11 14:45:46 · 6 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
f(x) = Ce^(-x) would be the form of an exponential decay curve.
This graph is decreasing and positive (as long as C is postive)
f'(x) = -Ce^(-x)
This graph is increasing and negative because it is essentially the initial graph reflected in the x axis.
So, yes, that is correct.
2006-10-11 14:52:35 · answer #1 · answered by z_o_r_r_o 6 · 0⤊ 0⤋
The derivative is the *rate of change* (or think of it as the slope) of the function. If the function is one of exponential decay, it's RATE of change is actually decreasing because as the function approaches the asymptote, it will sort of flatten out; and it is negative. But the slope is decreasing in the negative direction so it is getting less negative. Thus it is increasing and negative
2006-10-11 21:53:53 · answer #2 · answered by zmonte 3 · 0⤊ 0⤋
The function of an exponential is an exponential and negative if it is decaying.
2006-10-11 21:54:12 · answer #3 · answered by Brenmore 5 · 0⤊ 0⤋
an exponential decay would be something like e^(-x), whose derivative is -e^(-x)
2006-10-11 21:49:36 · answer #4 · answered by arbiter007 6 · 0⤊ 0⤋
I believe you are correct
2006-10-11 22:00:57 · answer #5 · answered by Dr. J. 6 · 0⤊ 0⤋
no
it is decreasing and negative
2006-10-11 22:15:20 · answer #6 · answered by gjmb1960 7 · 0⤊ 0⤋