1. The problem statement, all variables and given/known data Use the intermediate value theorem and rolles theorem to prove that the equation has exactly one real solution 2x-2-cos(x)=0 3. The attempt at a solution Let the interval be [a,b] and let f(a)<0 and f(b)>0 Then by the IVT there must be at least one zero between a and b. f'(x)=2+sin(x) since f'(x) doesnt = 0 anywhere and its always >0, therefore f(x) is increasing throughout its entire domain. Therefore f(a) cannot = f(b) anywhere. I feel like im doing a bad job at explaining this, but this is my first proof for class ever, other than geometry in highschool and i was bad at it. Is there anything terribly wrong or that could be improved upon at all?