Grade 11 maths investigation
1 answer:
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note that gradient = at x = a
calculate for each pair of functions and compare gradient
(a)
= 2x and
= - 1
at x = 4 : gradient = 8 and - 1 : 8 > - 1
(b)
= 2x + 3 and
= - 2
at x = 2 : gradient = 7 and - 2 and 7 > - 2
(c)
= 4x + 13 and
= 2
at x = - 7 : gradient = - 15 and 2 and 2 > - 15
(d)
= 6x - 5 and
= 2x - 2
at x = - 1 : gradient = - 11 and - 4 and - 4 > - 11
(e)
y = √x =
= 1/(2√x) and
= 2
at x = 9 : gradient = and 2 and 2 >
If x represents the length of the box, then 42-x will be the girth. Since the largest area for a given girth is that of a square, the side length of the square cross section is (42 -x)/4.
The volume as a function of package length is then
.. v(x) = x((42-x)/4)^2
This has a maximum at x=14. The corresponding volume is 686 in^3.
The volume as a function of package length is then
.. v(x) = x((42-x)/4)^2
This has a maximum at x=14. The corresponding volume is 686 in^3.