Question

Let f(t)= (t)^(1/2) +(1+t)^(1/2) -4; t=225/64, upon the interval (0,infinity);
Find the derivative of f(t), in order to prove Rolle's Theorem, that if f(a)=f(b), then there is at least one number c in (a,b) at which f'(c)=0, where (a,b) is (0, infinity)...so yeah

Answer 1

for Rolle's Theorem to apply, it must be continuous on a Closed Interval [a,b]. Idk why the interval would be (a,infinity). You need f(b) to be defined and f(infinity) does not exist as an actually number.