<p>Does ne one know where i can find the solutions to the free response from the AP Calculus BC exam 1994</p>
<p>Or maybe someone here can help with the problem:</p>
<p>Let f and g be functions that are differentiable for all real numbers x and that have the following properties.
i.) f '(x)= f(x) - g(x)
ii.) g '(x)= g(x) - f(x)
iii.) f(0)= 5
iv.) g(0)= 1</p>
<p>a.) Prove that f(x) + g(x)= 6 for all x.
b.) Find f(x) and g(x). Show all your work.</p>
<p>a) Add (i) and (ii) together, integrate, and use initial conditions to find constant of integration.</p>
<p>b) Since you know, f(x)+g(x)=6, substitute g(x)=6-f(x) into (i). Then, integrate. Use initial condition (iii) to find constant. Then plug f(x) into the result from (a) to get g(x).</p>