Homework Sourse32 1 Consider the functionon the interval Find the average
3-2 # 1
Consider the function![\"f(x)](\"//mathweb1.sandbox.csun.edu/webwork2_files/tmp/equations/f0/840005f76f62a98f8b3d5c8d08ac841.png\") on the interval![\"[](\"//mathweb1.sandbox.csun.edu/webwork2_files/tmp/equations/13/a734f78883567730f83d63b9c259331.png\") . Find the average or mean slope of the function on this interval.By the Mean Value Theorem, we know there exists a ![\"c\"](\"//mathweb1.sandbox.csun.edu/webwork2_files/tmp/equations/37/649eaebf498b1d580178aa5a871d121.png\") in the open interval![\"(](\"//mathweb1.sandbox.csun.edu/webwork2_files/tmp/equations/c0/c285fffa416489cc1dfb44c2ef39a11.png\") such that![\"f\'(](\"//mathweb1.sandbox.csun.edu/webwork2_files/tmp/equations/04/bbe4a4484edd469592f50e51de83eb1.png\") is equal to this mean slope. For this problem, there is only onethat works. Find it. |
Solution
average slope is just 1/(8-1)*(10*sqrt(8)+10-10*sqrt(1)-10)=1/7*(20*sqrt(2)-10)=2.612 f\'(c)=5/sqrt(c)=2.612 c=3.66
