## Calculus: Early Transcendentals 8th Edition

$f'\gt0$ and $f''\lt0$.
Take $f(x)$ to represent the national deficit mentioned. The national deficit is increasing. So first, the graph of $f$ representing the national deficit must be increasing, which means $f'\gt0$. Now we notice the phrase 'is increasing at a decreasing rate'. That means it increases less rapidly than it did befor. The graph therefore goes from increasing steeply to increasing less steeply. This means all the tangent lines are above the graph $f$. Therefore $f$ is a concave downward. (The image below represents a model of the graph) Therefore, $f''\lt0$.