Imagine a lidless box with height h and a square base whose sides have length x. The box must have a volume of 107107 ftcubed3. a. Find and graph the function​ S(x) that gives the surface area of the​ box, for all values of xgreater than>0. b. Based on your graph in part​ (a), estimate the value of x that produces the box with a minimum surface area. Question content area bottom Part 1 a. Determine the function​ S(x). A.Upper S left parenthesis x right parenthesis equals x squared plus StartFraction 107 Over x squared EndFraction Upper S left parenthesis x right parenthesis equals x squared plus StartFraction 107 Over x squared EndFractionS(x)=x2+ 107 x2 B.Upper S left parenthesis x right parenthesis equals x squared plus 4 x Upper S left parenthesis x right parenthesis equals x squared plus 4 xS(x)=x2+4x C.Upper S left parenthesis x right parenthesis equals StartFraction 107 Over x squared EndFraction Upper S left parenthesis x right parenthesis equals StartFraction 107 Over x squared EndFractionS(x)= 107 x2 D.Upper S left parenthesis x right parenthesis equals x squared plus StartFraction 428 Over x EndFraction Upper S left parenthesis x right parenthesis equals x squared plus StartFraction 428 Over x EndFractionS(x)=x2+ 428 x Your answer is correct. Part 2 Graph the function​ S(x). Choose the correct graph below. The graphs are displayed using a window size of​ [0,25,1] by​ [0,250,10]. A.

A coordinate system has a horizontal axis labeled from 0 to 25 in increments of 1 and a vertical axis labeled from 0 to 250 in increments of 10. From left to right, a curve starts at (0, 0), then rises at an increasing rate, passing through (1.5, 8), (3.2, 23), and (12, 192). All coordinates are approximate. B.

A coordinate system has a horizontal axis labeled from 0 to 25 in increments of 1 and a vertical axis labeled from 0 to 250 in increments of 10. From left to right, a curve falls steeply at a decreasing rate, passing through (1.5, 50) to a minimum at (3.2, 21), and then rises at an increasing rate, passing through (12, 145). All coordinates are approximate. C.

A coordinate system has a horizontal axis labeled from 0 to 25 in increments of 1 and a vertical axis labeled from 0 to 250 in increments of 10. From left to right, a curve falls steeply at a decreasing rate, passing through (3, 152) to a minimum at (6, 107), and then rises at an increasing rate, passing through (12, 180). All coordinates are approximate. Your answer is correct.D.

A coordinate system has a horizontal axis labeled from 0 to 25 in increments of 1 and a vertical axis labeled from 0 to 250 in increments of 10. A curve is above the horizontal axis and to the right of the vertical axis, approaching both. Part 3 b. xalmost equals≈enter your response here ​(Round to two decimal places as​ needed.)