find the absolute maximum and the absolute minimum of the given function?

Question

Find the absolute maximum and the absolute minimum of
F(t) = t^2/(t-1)
-2 is less than or equal to t and t is less than or equal to -1/2

Could someone break this down step by step for me - am lost.
Please help!!

Answer 1

First find the derivative



F'(t) = (t^2-2t)/(t-1)^2



Set F'(t) = 0 to find if where the max's and minimums are



0 = (t^2-2t)/(t-1)^2

0 = (t^2-2t)

0 = (t-2) t

Max/Min t=0 and t=2



You will also note that the function is discontinuous at t = 1 (the denominator is 0. This is also a point where you could find mas/min



Since your interval is -2 >= t >=-1/2, the max and the min will occur at the end points since t = 0, t=1 and t=2 are outside of your interval.



accordingly



F(-2) = (-2)^2/(-2-1)

F(-2) = -4/3



F(-1/2) = (-1/2)^2/ (-1/2 -1)

F(-1/2 = - 1/6



Min = -4/3 and Max = -1/6