7. Along all triangles in the first quadrant formed by the a-axis, the y-axis, and tangent lines to the graph of y = 3x-x2, what is the smallest possible area? Answer :_____________

8. A space probe in the shape of the ellipsoid 4x2+ y2+4z2 = 16 enters Earth's atmosphere and its surface begins to heat. After 1 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. Answer :____________