(a) \(y^\prime=2-4/\sqrt x=0\) gives x=4 and A=(4,−8). \(2x=8\sqrt x\) gives B=(16,0). (b) The line is above the curve for 4≤x≤16. \[A=\int_4^{16}\left[\frac{2x-32}{3}-2x+8\sqrt x\right]dx=\left[-\frac23x^2-\frac{32}{3}x+\frac{16}{3}x^{3/2}\right]_4^{16}=\frac{32}{3}.\] Alternatively, the area below the curve is 176/3 and the triangle below AB has area 48; their difference is 32/3.