Question

(8.5-2x)(11-2x)(x) what is the approximate value of x that would allow you to construct an

Answer 1

The largest volume possible from one piece of paper for open-top box is 64.296 cubic unit.

What is meant by the term maxima?

• The maxima point on the curve will be the highest point within the given range, and the minima point will be the lowest point just on curve.
• Extrema is the product of maxima and minima.

For the given question dimensions of open-top box;

The volume is given by the equation;

V = (8.5-2x)(11-2x)(x)

Simplifying the equation;

V = x(4x² - 39x + 93.5)

Differentiate the equation with respect to x using the product rule.

dV/dx = x(8x -39) + (4x² - 39x + 93.5)

dV/dx = 8x² - 39x + 4x² - 39x + 93.5

dV/dx = 12x² - 72x + 93.5

Put the Derivative equals zero to get the critical point.

12x² - 72x + 93.5 = 0.

Solve using quadratic formula to get the values.

x = 4.1  and x = 1.9

Put each value of x in the volume to get the maximum volume;

V(4.1) =  4.1(4(4.1)² - 39(4.1) + 93.5)

V(4.1) = 3.44 cubic unit.

V(1.9) = 1.9(4(1.9)² - 39(1.9) + 93.5)

V(1.9) = 64.296 cubic unit. (largest volume)

Thus, the largest/maximum volume possible from one piece of paper for open-top box is 64.296 cubic unit.

To know more about the maxima, here

brainly.com/question/17184631

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