If a rare antique appreciates over time according to f(t) = K (e^(t^0.5)) and the interest rate is r;
1) What would be the present value (PV) of selling it at time t?
2) What time of sale would maximise this present value?
For question 1, I used (e^(-rt)) so that PV = K(e^((t^o.5) - rt))
As for part two I have thought about several things such as taking natural logs of both sides first and differentiating twice and then making that equal to zero, but can't quite seem to make it work.
Ideas?
Thanks for anyone who can help me out in any way and sorry for the large use of bracketing but I wanted to make sure you guys (and gals) knew which parts where being raised to the power of which other parts.
Try only differentiating once then solving for where it equals 0. This will give you either the max or min of the function. Differentiating twice gives points of inflection.
LOL! Thanks Bob! Yeah for some reason I was thinking that differentiating twice would give me the max and mins. The twice differential looked scary to me and I was starting to worry so you've saved me a few minutes of stress. Nice one.
Differentiate a function f(x) once and equal the result to zero and then solve for x*. Differentiate again and replace x* in the result:
- If the second derivative result is positive, the function is concave and consequently has a point which is a minimum;
- If the second derivative result is negative, the function is convex and consequently has a point which is a maximum.
x* is then the minimal or the maximal value respectively.
Last edited by Rassis; Dec 14th, 2005 at 01:32 PM.
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