AP+Review+3-Problem+8

8. Let //f// and //g// be the functions given by //f(x)=////e^// //x// and //g(x)=lnx.//

 (a) Find the area of the region enclosed by the graphs of //f// and //g// between x= ½ and x=1.  (b) Find the volume of the solid generated when the region enclosed by the graphs of //f// and //g// between x= ½ and x=1 is revolved about the line y=4.  (c) Let //h// be the function given by //h(x)//=//f(x)-g(x)//. Find the absolute minimum value of //h(x)// on the closed interval ½ ≤x≤1, and find the absolute maximum value of //h(x)// on the closed interval ½ ≤x≤1. Show the analysis that leads to your answer.

Josh Massee: The work looks good but written justification s are necessary for the max's and min's in part (c).