Graphically determine which of the following functions

has larger values for **x** large.

Using

> plot(x^7,x=0..10,thickness=2);

> plot({x^7,4^x},x=0..10,y=0..10^7,thickness=2);

From the two graphs above, it appears that **y = x ^{7}** is the
answer. However, if we make

> plot({x^7,4^x},x=0..15,y=0..10^8,thickness=2);

Two alternative methods for doing this type of investigations are to
consider the graph of **y = x ^{7} - 4^{x}**:

> plot(x^7-4^x,x=0..50,y=-10..10,thickness=2);

or the graph of **y = x ^{7} / 4^{x}**:

> plot(x^7/4^x,x=0..50,y=0..2,thickness=2);