Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-$s ( t ) = \sqrt { t ( 3 - t ) } , \quad [ - 1,5 ]$

Question

Quizplus · Accepted Answer

The function $s(t) = \sqrt{t(3-t)}$ is not continuous on the entire interval $[-1,5]$ because it involves a square root of a negative number for $t > 3$ and $t < 0$, making it undefined for parts of the interval. The Mean Value Theorem requires the function to be continuous on the closed interval and differentiable on the open interval.

Determine Whether the Function Satisfies the Hypotheses of the Mean s(t)=t(3−t),[−1,5]s ( t ) = \sqrt { t ( 3 - t ) } , \quad [ - 1,5 ]s(t)=t(3−t)​,[−1,5]

Determine Whether the Function Satisfies the Hypotheses of the Mean $s ( t ) = \sqrt { t ( 3 - t ) } , \quad [ - 1,5 ]$