find the absolute maximum and minimum values of the following function on the given interval. then graph the…

find the absolute maximum and minimum values of the following function on the given interval. then graph the function and identify the points on the graph where the absolute extrema occur. h(x)=2\\sqrt3{x}, - 1\\leq x\\leq8. find the absolute maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete the choice. a. the absolute maximum value 4 occurs at x = 8. (use a comma to separate answers as needed.) b. there is no absolute maximum. find the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete the choice. a. the absolute minimum value occurs at x =. (use a comma to separate answers as needed.) b. there is no absolute minimum.

find the absolute maximum and minimum values of the following function on the given interval. then graph the function and identify the points on the graph where the absolute extrema occur. h(x)=2\\sqrt3{x}, - 1\\leq x\\leq8. find the absolute maximum. select the correct choice below and, if necessary, fill in the answer boxes to complete the choice. a. the absolute maximum value 4 occurs at x = 8. (use a comma to separate answers as needed.) b. there is no absolute maximum. find the absolute minimum. select the correct choice below and, if necessary, fill in the answer boxes to complete the choice. a. the absolute minimum value occurs at x =. (use a comma to separate answers as needed.) b. there is no absolute minimum.

Answer

Explanation:

Step1: Evaluate the function at endpoints

First, find (h(-1)) and (h(8)). The function is (h(x)=2\sqrt[3]{x}). When (x = - 1), (h(-1)=2\sqrt[3]{-1}=2\times(-1)=-2). When (x = 8), (h(8)=2\sqrt[3]{8}=2\times2 = 4). Since the function (y = \sqrt[3]{x}) is a continuous function on the interval ([-1,8]) and its derivative (y'=\frac{2}{3x^{\frac{2}{3}}}) is non - zero on the open interval ((-1,8)) (the derivative is undefined at (x = 0) but the function is continuous there), we only need to consider the values of the function at the endpoints of the closed interval ([-1,8]).

Step2: Determine the minimum value

We have (h(-1)=-2) and (h(8) = 4). Since (-2<4), the absolute minimum value of (h(x)) on the interval ([-1,8]) is (-2) and it occurs at (x=-1).

Answer:

A. The absolute minimum value (-2) occurs at (x=-1).