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Mon 3 May, 2010 02:33 pm
Q. 1 A function f (t) depends on two variables a and b according to the equation
f (t) = a (t) e ^ b (t). At one point in time, a =3 and is decreasing at a rate of 4 units per second. At the same point in time, b=1 and is increasing at a rate of 2 units per second. If f(t) increasing or decreasing at that moment?
@AQ,
You want to find the sign of
f(t) at that time. What you are given is the the function implicitly written as a function of time:
f (t) = a (t) e ^ b (t)
so take the derivative with respect to
t:
f '(t) = a '(t)e^b(t) + a(t)b '(t)e^b(t)
Now put
a(t) = 3
a '(t) = -4
b(t) = 1
b '(t) = 2
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