Homework SourseFind the exact global maximum and minimum values of the func
Find the exact global maximum and minimum values of the function g(t)=(5te^-2t) if t > 0.
global maximum at t=
global minimum at t=
(Enter none if there is no global maximum or global minimum for this function.)
global maximum at t=
global minimum at t=
(Enter none if there is no global maximum or global minimum for this function.)
Solution
g(t)=(5te^-2t) if t > 0 g\' = 5e^-2t + 5te^-2t(-2) g\' = (5 - 10t)e^-2t t > 0 g\'\' = -10e^-2t + (5-10t)e^-2t(-2) g\'\' = 20(t-1)e^-20t g\' = 0 => t = 1/2 g\'\'(1/2) < 0 => t = 1/2 is maxima no other critical points then global maxima at t=1/2 global minima : none
