6. (15 pts) Evaluate dy dx, where R is thesemicircular region bounded by the x-axis and the curve y = , |x| ≤ 1.

4. (15 pts) A space probe in the shape of the ellipsoid 4x2 + y2 + 4z2 = 16 enters the earth's atmosphere and its surface begins to heat. After one hour, the temperature at the point (x,y,z) on the probe's surface is T(x, y, z) = 8x2 + 4yz - 16z + 600.Find the hottest point on the probe's surface.