10 Application. A catenary arch is the curve traced out by a flexible cord hanging from two fixed points at the same height. Mathematically, the equation of a catenary is defined by the differential equation, f" (2 ) -V1 - (f' (2) ) 2, (*) a for some constant parameter a. Consider the curve, y = 18 + 25 cosh 25 Use desmos or similar software to graph this curve from x = -25 to x = 25. Then differentiate y to demonstrate that this function is a solution to the catenary equation () when a = 25.10) f " ( x ) = 3 /1 - (f ( x ) ) ? 4 = 18+ 25 cosh 25 4' = 25 sinh 25 = Sinh - 23 4 ( - 25) = 56.58 y ( 25 ) = 56 .58 4 ( 0 ) = 43