Determine whether the function satisfies the hypotheses of the Mean Value Theorem for the given interval.
-$$s ( t ) = \sqrt { t ( 4 - t ) } , \quad [ - 1,5 ]$$

Question

Quizplus · Accepted Answer

The function $s(t) = \sqrt{t(4-t)}$ is not continuous on the entire interval $[-1,5]$ because it involves a square root of a negative number for $t < 0$ and $t > 4$, violating one of the necessary conditions for the Mean Value Theorem.

Determine Whether the Function Satisfies the Hypotheses of the Mean s(t)=t(4−t),[−1,5]s ( t ) = \sqrt { t ( 4 - t ) } , \quad [ - 1,5 ]s(t)=t(4−t)​,[−1,5]

Determine Whether the Function Satisfies the Hypotheses of the Mean $s ( t ) = \sqrt { t ( 4 - t ) } , \quad [ - 1,5 ]$