verify that the function satisfies the three hypotheses of rolle's theoreom on the given interval then find all numbers c that satisfy the conclusion of rolle's theorem.

Question

1) 5-12x+3x^2 [1,3]

Answer 1

To see if Rolle's theorem applies, check
1. if the function is continuous on the closed interval [a, b].
2. if it is differentiable
on the open interval (a,b).
Furthermore,
3. check if f(a)=f(b).

If all the above conditions are satisfied, then there exists some value c between a and be such that f(c)=0.