A container company is designing a square based, rectangular box that will have a volume of 8m3. This is a closed box! So you have 4 sides, the square bottom and the square top. (a) Let x and y be the dimension of the box. Find a formula for S(x), the surface area of the box as a function of x. (b) Find the critical point(s), and vertical asymptotes. Make a table, and sketch S(x) on (0, +∞). (c) What should be x and y to minimize the surface area of the box? What is the minimum surface area? Describe what the box looks like.

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A: Please refer the attached image for complete solution.

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Q: Find and classify the critical points off (x) = 6x°(5 – x)° as local maxima and minima.

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Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

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Q: Find the critical numbers of the function.   g(t)  =| 3t - 4  |

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.