hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM

Now press and scroll down the screen to:

 

1

→

------------------

 

(x + 2)2

Now press to obtain the table of variations.

If you are not in step-by -step mode, you can also get the calculation of the derivative by typing:

DERVX(G(X))

which produces the preceding result.

To prove the stated inequality, first calculate g(0) by

typing G(0) and pressing

. The answer is:

3

-- .

 

 

2

Now calculate g(2) by typing G(2) and pressing

.

The answer is

7

 

 

-- .

 

 

 

4

 

 

The two results prove that:

 

3

7

x ∈ [0,2]

 

-- ≤ g(x) ≤

-- for

 

2

4

 

 

Solution 2

 

 

 

The calculator is not needed here. Simply stating that:

x

--

en ≥ 0 for x ∈ [0,2]

is sufficient to show that, for x ∈ [0,2] , we have:

xx

3 -- -- 7 --

--en ≤ g(x)en ≤ --en

24x

Solution 3

To integrate the preceding inequality, type the expression at the right:

Pressing produces the result at the right:

16-24

 

 

Step-by-Step Examples