# Miguel is designing shipping boxes that are rectangular prisms. the shape of one box, with height h in feet, has a volume defined

Miguel is designing shipping boxes that are rectangular prisms. the shape of one box, with height h in feet, has a volume defined by the function v(h)=h(h-5)(h-6). graph the function. what is the maximum volume for the domain 0

The zeros are 5 and 6 on the graph and it looks like it is going the opposit way

the answer is 24 ft^3. I just took the connexus quiz trust me!

Step-by-step explanation:

24ft³ hope this helps!!!

105 cubic foot

Step-by-step explanation:

We have given with the function:-

V(h) = h(–h + 10)(–h + 8)

1) Let's simplify the function by applying distributive property to the right side

V(h) = h(–h + 10)(–h + 8)

= {h(-h) + h(10)}(-h+8)

= (-h²+10h)(-h+8)

= (-h²)(-h)+(-h²)(8)+(10h)(-h)+(10h)(8)

= -8h²-10h²+80h

V(h)   = - 18h² + 80h

2) Let's plugin the value of h from 1 to 9 (since 0<h<10) into the function V(h)   = - 18h² + 80h and create a table as shown below:-

h V(h)

163

296

3105          <-------------maximum volume

496

575

648

721

80

9  -9

Looking at the above table, we can conclude the maximum volume for the domain 0<h<10 is 105 cubic foot.

24ft³

is the answer to the equation

whole quiz

1. 4x(x-4)(x+6)

2.0, -2, -5 the third graph

3.  the number o is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1.

4.the relative maximum is at (-1.53, 12.01) and the relative minimum is at (1.2,-8.3)

5. 105 ft^3

your welcome!  5 stars it,  so everyone knows i'm correct

Step-by-step explanation:

Tha function means that the dimensions of the rectangular base are h -10 and h - 8.

Both of them have to be greater than zero and the height must also be greater than zero

Then the domain are all those h for which h >0, h - 8 > 0 and h - 10 > 0

Solve that system h >0, h>8 and h>10

The solution is the condition that meets all the inegualities and it is h > 10

Then the domain is  all the real values greater than 10.

Use the First Derivative Test to find the value of h that maximizes V(h).

V(h) = h(h - 10)(h - 8)

V(h) = h^3 - 18h^2 + 80h

V'(h) = 3h^2 - 36h + 80

0 = 3h^2 - 36h + 80

h = 2.9449495367

--or--

h = 9.0550504633

So those are your critical points. Both of those values are within the domain of h, so now we turn to the Second Derivative Test to find out which one is a maximum.

V''(h) = 6h - 36

V''(2.9449495367) = -18.33

V''(9.0550504633) = 18.33

A local maximum occurs where the second derivative is less than zero (and likewise, a minimum occurs where the 2nd derivative is greater than zero). Hence, the maximum volume occurs at h=2.9449495367. Sticking that into V(h) gives:

V(2.9449495367) = 105.0276

The answer then rounds to 105ft³

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