Let f be a real-valued function that is continuous on [0, 1] and differentiable on (0, 1) and let g be a function defined on (0, 1] by g(x) = f(x) == x. if f(0) = 0, $(") == and f(1) = 0, (i) show that there exists c ir such that g(c)=0.
(ii) determine whether the equation g'(x) = 0 has any real root in (0,1). justify your answer.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: