Rolle's Theorem and a Constant Function
Which of the following statements correctly describes the application of Rolle’s Theorem to the function $$f(x)=5$$ on the interval $$[-2,3]$$?
A
Even though $$f(-2)=f(3)$$, there exists a unique point in $$(-2,3)$$ where $$f'(x)$$ reaches its maximum value.
B
Since $$f(x)=5$$ is constant with $$f(-2)=f(3)$$, Rolle’s Theorem guarantees that every point in $$(-2,3)$$ is a point where $$f'(x)=0$$.
C
The constant function $$f(x)=5$$ does not satisfy the differentiability condition required by Rolle’s Theorem, so the theorem does not apply.
D
Rolle’s Theorem cannot be applied because constant functions do not have any critical points.
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