Demostrate rolle's theorem using f(x)=x sin(x) on the interval [0,π].

Rolle's theorem: if a function is continuous on the interval  and  differentiable on the interval , and  , then there's at least one point  in interval  which makes for your function: is continuous and differentiable everywhere. it is a product of two continuous functions (there are no non-permissible values, we check to see if the value of  at the end points are equal.since  , the hypotheses of rolle's theorem can be applied here.  (it's not easy to solve this algebraically. if you graph this, there is clearly a point where the tangent line has a slope of 0. below i stop where i can't do much more)set  to 0 and solve.