HP 15c Scientific manual 003 004 005 007, X + 8, 008 009, 6 x + 8, 010 011 012 013 014

190 Section 13: Finding the Roots of an Equation

Keystrokes	Display
-	003–	30
*	004–	20	(x – 6) x.
8	005–	8
+	005–	40
*	007–	20	((x – 6) x + 8) x.
4	008–	4
*	009–	20	4 ((x – 6) x + 8) x.
7	010–	7
.	011–	48
5	012–	5
-	013–	30
n	014–	43 32

It seems reasonable that either a tall, narrow box or a short, flat box could be formed having the desired volume. Because the taller box is preferred, larger initial estimates of the height are reasonable. However, heights greater than 2 decimeters are not physically possible (because the metal is only 4 decimeters wide). Initial estimates of 1 and 2 decimeters are therefore appropriate.

Find the desired height:

Keystrokes	Display
¥		Run mode.
1 v	1.0000	Initial estimates.
2	2
´ _ 3	1.5000	The desired height.
)	1.5000	Previous estimate.
)	0.0000	f(x) at root.