Chapter 1.3, Problem 64E

Solution

(a)

To find: The order from least to great

  $\sqrt{x}<x<x^2$

Given information:

The function is in the following order from least to greatest.

  $\sqrt{x}<x<x^2$

(b)

To find: The graph of $\sqrt{x},x{x}^2$

Graph is given

Given information:

  

The graph confirms in the response (a)

(c)

To find: The graph of $\sqrt{x},x{x}^2$ in viewing window (0,2) and (0,1.5)

Graph is given

Given information:

Graph is given below

  

(d)

To find: The positive value of x that satisfies the condition in (a).

As we can see that for x=4 $\sqrt{x}<x<x^2$

Given information

Let x=4$f(4)=\sqrt{4}=2$

  $f(4)=4^2=16$

  $\begin{array}{l}f(x)=x\\ f(4)=4\end{array}$

As we can see that for x=4 $\sqrt{x}<x<x^2$

But for $0\le x\le 1$

  $\sqrt{x}>x>x^2$