(a) Find the average value of the function $\displaystyle f(x)= \frac{2x}{(1+x^2)^2}$ on the interval $[0, 2]$.

$f_{ave} =$

(b) Use a calculator, computer, or the graph of $f$ to find two values of $c$ such that $f_{ave}=f(c).$ List these values in increasing order. Make sure your answers are correct to three decimal places.

Smaller value of $c =$

Larger value of $c =$