Calculus: Early Transcendentals 8th Edition

$f'\lt0$ and $f''\gt0$.
Take $f(x)$ to represent the SAT scores mentioned. SAT scores are declining at a slower rate. So first, the graph of $f$ representing SAT scores must be declining, which means $f'\lt0$. Now we notice the phrase 'decline at a slower rate'. That means it declines less rapidly than it did before. The graph would therefore go from decreasing steeply, to decreasing less steeply. This means all the tangent lines are below the graph $f$. There is a concave upward here. (The image below represents a model of the graph) Therefore, $f''\gt0$.