Second Derivatives and Beyond
This part is as fun as it sounds. It's like those connect-the-dots games on restaurant placemats. Maybe not exactly like them, no sweet bear or zebra shapes (most likely), but we know the dots go in order from left to right, and we're supposed to connect the dots with particular shapes.
The function f hits the points (0,0) and (1,4) and is increasing & concave up from x = 0 to x = 1. We have two dots:
We have a shape:
We connect the dots with the shape:
That's all there is to it.