Solve using derivatives. I have no clue where to start on this I really need help please.
Please show steps and diagram.

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx  where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V =  8x^2 - x^4 / 4x

V =  2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 =  0  for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the  length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume =  0.816 *  2.667 =  2.177 m^2.

The answers are correct to the nearest thousandth.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17