Chapter 4.4, Problem 188E

For the following exercises, use a calculator to graph the function over the interval [a, b] and graph the secant line from a to b. Use the calculator to estimate all values of c as guaranteed by the Mean Value Theorem. Then, find the exact value of c, if possible, or write the final equation and use a calculator to estimate to four digits.

188. [T] $y=x+\frac{1}{x}\text{over}\left[\frac{1}{2},4\right]$