Final answer:
Rolle's Theorem applies to the interval [1,2] for the function plot that shows a horizontal line from (0,3) to (3,3), as it satisfies the necessary conditions of the theorem.
Step-by-step explanation:
The student's question pertains to Rolle's Theorem, which states that if a function f(x) is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), and if f(a) = f(b), then there exists at least one number c in the open interval (a, b) such that the derivative f'(c) = 0. To apply Rolle's Theorem to any given interval, we need the endpoints of the function’s graph on that interval to be at the same vertical height, indicating they have the same function value.
Looking at the descriptions provided of different function plots:
The plot from (0,2) to (3,8) has different function values at its endpoints, so Rolle's Theorem does not apply.
The plot from (0,3) to (3,3), however, is a horizontal line, which means f(0) = f(3), satisfying the condition for Rolle's Theorem.
Therefore, Rolle's Theorem applies to the interval [1,2], since this interval falls within the endpoints of the horizontal line plot, which has equal function values at its endpoints and is differentiable in between.