HP 40gs User Manual page 298

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