Show that the turning points of ef(x) occur for the same values of x as the turning points of f(x).

Find all the turning points of x1/x for x > 0 and decide whether each is a maximum or minimum. Give a sketch of the graph of y = x1/x for x > 0. Deduce from your sketch that

lim
x® ¥ 
 x1/x =
lim
n® ¥ 
 n1/n.

Now use the result from the problem Discrete Trends to find this limit.

Show that

lim
x ® 0 
 x1/x = 0
by substituting t=1/x. Hence find the largest value of c such that the line y=c lies under the graph of y=x1/x.