Consider the function in the closed interval .If the value guaranteed by the Mean Value Theorem in the closed interval is ,then what is the value of ? Round your answer to 3 decimal places.

Question

Consider the function  ​ in the closed interval  .If the value guaranteed by the Mean Value Theorem in the closed interval is  ,then what is the value of  ? Round your answer to 3 decimal places. ​

Quizplus · Accepted Answer

According to the Mean Value Theorem, there exists a point c in the closed interval such that the derivative of the function at c is equal to the slope between the endpoints. Therefore, since the value guaranteed by the Mean Value Theorem is positive, the function is increasing on the closed interval. This means that the value of the function at the right endpoint is greater than the value at the left endpoint. Since the function is continuous, the Intermediate Value Theorem tells us that there must be a point between the endpoints where the function is equal to the value guaranteed by the Mean Value Theorem. Therefore, the value of the function at 11eac44f_ee38_02df_bedf_a5cbb0f9b234_TB7497_11 must be greater than the value guaranteed, and since the function is increasing, the answer is choice B, 1.338.

Consider the Function ​ in the Closed Interval

Consider the Function in the Closed Interval