a) Find the average value of f(x) = 1/sqrt(x) on the interval [4,9]. I didn't have a problem with this part; I got 2/5 which checks with the answer sheet. My problem is with part (b).

b) Find the value(s) of x on [4,9] where the function takes on its average value.

Question

a) Find the average value of f(x) = 1/sqrt(x) on the interval [4,9].    I didn't have a problem with this part; I got 2/5 which checks with the answer sheet. My problem is with part (b).

b) Find the value(s) of x on [4,9] where the function takes on its average value.

jdoe0001 · Answer

ok.... so you got the average value for "y" is 2/5.... so b) it's just saying, ok, now plug that back in the original function, and solve for "y"

jdoe0001 · Answer

$\bf y=\cfrac{1}{\sqrt{x}}\qquad \textit{average value between  }[4,9]\implies \cfrac{2}{5}\ \quad \
\cfrac{2}{5}=\cfrac{1}{\sqrt{x}}\qquad \textit{solve for }x$