HP 40gs - Manual (Page 298)

16-24 Step-by-Step Examples
Now press and scroll down the screen to:
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: .
Now calculate g(2) by typing G(2) and pressing .
The answer is .
The two results prove that:
for
Solution 2
The calculator is not needed here. Simply stating that:
for
is sufficient to show that, for , we have:
Solution 3
To integrate the preceding
inequality, type the
expression at the right:
Pressing produces
the result at the right:
1
x 2 + ( )
2
------------------- →
3
2
---
7
4
---
3
2
--- g x ( ) 7
4
--- ≤ ≤ x 0 2 [ , ] ∈
e
x
n
---
0 ≥ x 0 2 [ , ] ∈
x 0 2 [ , ] ∈
3
2
---e
x
n
---
g x ( )e
x
n
---
7
4
---e
x
n
---
≤ ≤
hp40g+.book Page 24 Friday, December 9, 2005 1:03 AM