1. The problem statement, all variables and given/known data Show that there exists one root int (0,2) of the following function: f(x)=(1-x^2)^2-√((1-x^2)*(1-1/2*x^2)) 2. Relevant equations 3. The attempt at a solution I first found: f(0)=0 and f(2)=7.268 But, i don't know what to do now. I'm not sure if it has something to do with the mean value theorem or not, or if i have to differentiate or not. Any ideas will be very much appreciated. Thank you.