Answer to Question #60677 in Real Analysis for esita

Question

5. a) Show that the local maximum value of
x
x





 1
is e
e
/1
. (4)
b) Verify Cauchy Mean Value Theorem for the functions
, ,1[ ]4
1
( ) = , ( ) = x∈
x
f x x g x . (3)
c) Show that [ 1+ x ≤ e , ∀x ∈ ,0[ ∞
x
. Does the inequality hold for x < 0 ? Justify your
answer.