Second, the number line sign analysis summaries will help identify the shape of the graph. Imagine taking the unit circle and breaking it up according to quadrants. The signs of f '(x) and f ''(x) determine which of these four basic shapes the graph is most like.

- f '(x) = + and f ''(x) = + means f(x) looks like Quadrant IV (incr, conc. up)
- f '(x) = - and f ''(x) = + means f(x) looks like Quadrant III (decr, conc. up)
- f '(x) = + and f ''(x) = - means f(x) looks like Quadrant II (incr, conc. down)
- f '(x) = - and f ''(x) = - means f(x) looks like Quadrant I (decr, conc. down)

However, sign analysis does not tell us the heights of any points. The problem gives only one point: f(0) = 1. The rest of the points of interest (especially the local extreme values) can be found by thinking about the information relating to the areas of the graph of f '(x). (Again, think about the Fundamental Theorem of Calculus).

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