Answer:



Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4
. The volume of a cylinder is given by

Equating it to 4

Let's solve for h

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

Replacing the formula of h

Simplifying

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

Rearranging

Solving for r

![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is


(4y + 1)(y + 6)
I don't know what you mean by proper location
It shouldn't matter what order the factors are in.
Answer:
Y=8x-4
Step-by-step explanation:
2x -1/4y= 1
2x -1 = 1/4 y
4(2x -1) =y
8x -4 = y
Answer:
slope of line pass throught jk is 0.5 slope
since line perpendicular to jk then x × 0.5= -1 so slope of line perpendicular is -2
then eq of line is y= -2x -15
Answer: No
Step-by-step explanation: The way that you know is you put the #s from least to greatest 3,9,14 then add the 2 smallest #s and if it is greater than the biggest #it does make a triangle so it would be 12<14 and that is false .