Question

HELP PLEASE

For this question you must see the attached document. Find an equation of a polynomial whose graph connects the green dots (at points (0,0) and (10, 9)), stays entirely within the large black frame for x values between 0 and 10, and does not touch any of the black squares in the picture. For full credit, you must explain how you used skills you learned in this course to find your equation. 9 8 7 6 5 4 3 z 3 2 3 41 S 6 10 a 8

Answer 1

To find: An equation of a polynomial whose graph connects points (0,0) and (109) the large black frame & stays entirely worthin for values between O and lo, soin This method is a trial method, first we have to approximale a werve black boxes setting menima & maxima at 2 points such that it does ng touch any of the boxes and joins two end poining we must try to pass the curve through the difficult gap lie. boxes with kast gap) & setting minimal maxima ar 'some point between them would help. There will be many ways & many polynomial equation that can satisfy this problema for this problem). Here B one my solution (poly eqn * Suppose the polynomial polynomial is flue). setting Critical poimis at x=3,52% & x26.5='/ Then f cu) = K (x-72) (11/2) / there, KER but not a polynomisy Since I've mentioned exactly 2 Critical points. & K is anypostire nal

checking for maxima & monima for poly, of cm) we have, f(x) = k (x-7)(n-12) KER So, t"() = [(4-2)-1 (1-12) = k120-9 f"(x)] 2 K 17-9) -2K co V 22 포 per cessamente 2 k (11-9) - 2K yo local Hence, local minima have at x 2 we 24 & maxima at uzla How Since, f' CM) ~ K (x-7)(x-"%) 2 K [m- qx + ) we have to find the polynomial fen) f(x) = no qxp 2 K Sk [=ax 77] de Ei au n ) + [ 47-5412 *** 2313] ?C + c feng K 12

But The polynomial poirs (01016 (10,9) moss pass through the =) Czo At xeo, y f(n) = f(6)zo Klo]+ 1620 fra), 1482 - 54172312) Thus, At na 10 feres flo) 29 > [ 4 (109) – 54(10)° +231600)) = 9 2) k (910)=9 og = 54 910 455 i The polynomial that is required is feny १ 2 [ 422-542+72312 910 with other Condo & a valves beta re osne lo plotting this poly compay ne conditions for boxes o & lo in Desmos , (we.got ar required resor or polynomial curve) i frete-657 Ys7C15* *** susest a fossy eas {34044} city geys Asasnau} 9 Eyes { bis Ly 27.8} w gay s3 {8.554 29.5] (väg brey 27.5 | Srengoas) i sreyers losens 205) } لاية

101 - 5. 0 5 10
By plotting the polynomial equation along with boundary conditions and all conditions for boxes in DESMOS, We clearly see that this is the polynomial that satisfies the given conditions and one of the solution for this problem.

Hope it helps.