For 0≤x≤5, the quantity A(x)=x(10−2x) represents the area, in square units, of a region whose linear dimensions depend on x.
(a) Compute A′(x).
(b) Find all critical points of A in the interval [0,5].
(c) Determine the value of x that yields the maximum area and calculate that maximum. Justify your conclusion using an appropriate calculus test.