Posted by Anonymous on Sunday, November 3, 2013 at 5:02pm.
Find the absolute maximum and absolute minimum values of f on the given interval.
f(t) = (36 − t^2)^ 1/t, [−1, 6]

calculus  Reiny, Sunday, November 3, 2013 at 5:54pm
nasty equation, none of the standard methods of derivatives fit.
I am going to take logs of both sides
ln y = ln (36 t^2)^(1/t)
= (1/t)(ln (36t^2)
now product rule on right side
(dy/dt) / y = (1/t)(2t)/(36t^2) + (1/t^2)(ln(36t^2) )
dy/dt = y[(1/t)(2t)/(36t^2) + (1/t^2)(ln(36t^2) )]
so y = 0
(36t^2)^(1/t) = 0
there is an intuitive solution of t = 6
or
(1/t)(2t)/(36t^2) + (1/t^2)(ln(36t^2) ) = 0
2/(36t^2) = ln(36t^2) /t^2
ln(36t^2) = 2t^2/(36t^2)
what a messy equation, ran it through Wolfram
and there are no real solutions, (4 complex)
http://www.wolframalpha.com/input/?i=solve++log%2836t%5E2%29+%3D+2t%5E2%2F%2836t%5E2%29
unless I made an algebraic error or typo
so evaluate f(6) which happens to be at the end of your interval.
f(6) = (3636)^(1/6 = 0
Also evalute f(1) to see which is the max or min.
f(1) = (36  1)^1
=1/35 = appr .02857
Answer This Question
Related Questions
 Calculus (pleas help!!!)  Find the absolute maximum and absolute minimum ...
 Calculus (pleas help!!!)  Find the absolute maximum and absolute minimum values...
 Calculus Help Please!!!  Find the absolute maximum and absolute minimum values ...
 Calculus 1  Find the absolute maximum and absolute minimum values of f on the ...
 calculus  Find the absolute maximum and absolute minimum values of f on the ...
 Calculus Help Please!!!  Find the absolute maximum and absolute minimum values ...
 Calculus Help Please!!!  Find the absolute maximum and absolute minimum values ...
 Calculus Help Please!!!  Find the absolute maximum and absolute minimum values ...
 Calculus Help!  Find the absolute maximum and absolute minimum values of f on ...
 Calculus  Find the absolute maximum and absolute minimum values of the function...
More Related Questions