Answer:
13058.83 cubic inches
Step-by-step explanation:
Given that a rectangular box is having dimensions as 41x81 inches.
Let x be the side of square cut from all the four corners.
The open box made would have height as x and length 41-2x with width 81-2x
Volume =
Equate first derivative to 0
We get applicable root as x = 8.642
Max volume = 13058.83 cubic inches
Answer:
A) y = 3(x -3)^2 -46
B) (3, -46)
C) look at the y-coordinate of the vertex
Step-by-step explanation:
A) Factor the leading coefficient from the variable terms.
y = 3(x^2 -6x) -19
Inside parentheses, add the square of half the x-coefficient. Outside, subtract the same value.
y = 3(x^2 -6x +9) -19 -3(9)
y = 3(x -3)^2 -46
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B) Compared to the vertex form, ...
y = a(x -h)^2 +k
we find a=3, (h, k) = (3, -46).
The vertex is (3, -46).
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C) The vertex is an extreme value (as is any vertex). The sign of the leading coefficient tells you whether the parabola opens upward (+) or downward (-). This parabola opens upward, so the vertex is a minimum.
If the leading coefficient is positive, the y-coordinate of the vertex is a minimum. If the leading coefficient is negative, the y-coordinate of the vertex is a maximum.
