Acardboard box manufacturing company is building boxes with length represented by x+ 1, width by 5- x, and height by x -1. the volume of the box is modeled by the function below v(x) 18 14 10 6 24 x 5 6 2 2 3 -2 -6 over which interval is the volume of the box changing at the fastest average rate? [1,2] a. [1,3.5 b. c. [1,5] r0,3.51 d

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

Step-by-step explanation:

Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:

For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate

a. [1,2]

b. [1,3.5]

c. [1,5]

d. [0,3.5]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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