Final answer:
Sketch a function b(x) that is concave up to the left of x=3 and concave down to the right of x=3, resembling a parabola with a vertex at x=3.
Step-by-step explanation:
The student is asking to sketch a function b(x) that is concave up on the interval (-, 3) and concave down on the interval (3, -). To fulfill this request, you need to create a graph where the curve is shaped like a cup (concave up) to the left of x = 3 and shaped like a cap (concave down) to the right of x = 3. An example of such a function could be b(x) = -x^2 + 6x, which has a maximum at x = 3.
The graph would start by curving upwards as it approaches x = 3 from the left and then start curving downwards as it moves to the right of x = 3. The point at x = 3 would be the highest point on the graph and act as the vertex of the parabola, making it the transition point between concave up and concave down.