Match slope and concavity intervals on a cubic graph

Match to the fourth printed set: $x<-3.46$ or $x>3.46$, using the graph’s rounded labels. The Teacher arrow connects (a) to this last choice. Independently, $y^{\prime}=0.3x^2-3.6$ is positive for $x<-2\sqrt3$ or $x>2\sqrt3$. These are the exact open intervals; 3.46 is a rounded boundary, not an exact derivative root.

Match to the first printed set: $-3.46<x<3.46$ as displayed on the source graph. The exact derivative-sign interval is $-2\sqrt3<x<2\sqrt3$. The Teacher arrow links (b) to the first choice. Do not turn the rounded bound into an exact assertion about inputs between 3.46 and $2\sqrt3$.

Match to the third printed set: $x>0$. The Teacher arrow is horizontal from (c) to this choice. The independent check $y^{\prime\prime}=0.6x>0$ agrees.

Match to the second printed set: $x<0$, following the Teacher arrow. Here $y^{\prime\prime}=0.6x<0$. The printed turning coordinates are $(-3.46,8.31)$ and $(3.46,-8.31)$; exact values are $(-2\sqrt3,4.8\sqrt3)$ and $(2\sqrt3,-4.8\sqrt3)$. The original graph also marks x-intercepts $-6,0,6$.