For what values of `a in [0, 1]` does the area of the fiqure bounded by the graph of the function `y=f(x)` and the straight lines `x = 0 x = 1 & y = f(a)` is at a minimum & for what values it is at a maximum if `f (x) = sqrt(1-x^2)` Find also the maximum & the minimum areas.

Answer

`a = 1/2 ` gives minima, `A(1/2) = (3sqrt(3)-pi)/12 ; a = 0 ` gives local maxima` A(0) = 1 – pi/4 ; a = 1 `gives maximum value, `A(1)= pi/4`