Find the value of c which satisfies Rolle’s Theorem for the function f(x)=sin(x²) on (0,√π).

Answer 1

ok, if true, there must be two points that are the same, and somewhere in between those points, the derivaative must be zero.

sin(X^2)=0 At 0, and at sqrt(PI)
f'=2xcosx^2=0 at 0 and at sqrt(PI/2)
c=sqrt(PI/2)