The designer selects a cutout length that results in a valid

The designer selects a cutout length that results in a valid box. If he then increases the cutout length a small amount, the volume of the box Select an answer will increase then decrease will decrease may increase or decrease will increase  

Use your function from part (b) to determine the volume of the box when the side length of the square cutouts is 2.6 inches? Express the output value both with function notation and as a numerical value (for example k(8)=5k(8)=5 ).
   

Which of the lettered segments on the graph represents a change in square side length of 0.5 inches? If there aren\'t any, enter N. If there are multiple answers, enter them as a list separated by commas.

Which of the lettered segments on the graph represents a change in cutout side length that starts at a cutout length 0.5 inches? If there aren\'t any, enter N. If there are multiple answers, enter them as a list separated by commas.

Choose the appropriate notation, compute the exact value using the function definition, and choose the appropriate units.
Segment f: Select an answer x V Delta x Delta V   =  Select an answer inches square inches cubic inches  
Segment h: Select an answer x V Delta x Delta V   = Select an answer cubic inches square inches inches

Solution

a) valid box, => x>0

the volume of the box may increase or decrease

if x<1.86, with slight increase in x , volume increases

if x>1.86, with slight increase in x , volume decreases

b)

length of box=10-2x, width of box =13-2x, height of box =x

volume, k(x)= x(10-2x)(13-2x)

c)

when the side length of the square cutouts is 2.6 inches

volume,k(2.6)=2.6*(10-2*2.6)*(13-2*2.6)

volume,k(2.6)=97.344 cubic inches

d)

a,e,g represents a change in square side length of 0.5 inches

e)

b,f,h represents change in cutout side length that starts at a cutout length 0.5 inches

f)

segments labeled \'f\' represent a change in volume in  cubic inches

segments labeled \'h\' represent a change in volume in  cubic inches