Task 800
Task 800: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Part of the graph of $f(x) = ax^3 + bx^2 + cx + d$ is shown. What is $b$? asy unitsize(1.5 cm); real func(real x) { return((x + 1) (x - 1) (x - 2)); } draw(graph(func,-1.1,1.5))…
The task
Part of the graph of $f(x) = ax^3 + bx^2 + cx + d$ is shown. What is $b$? [asy] unitsize(1.5 cm); real func(real x) { return((x + 1)*(x - 1)*(x - 2)); } draw(graph(func,-1.1,1.5)); draw((-1.5,0)--(1.5,0),Arrows(6)); draw((0,-1)--(0,2.5),Arrows(6)); label("$x$", (1.5,0), E); label("$f(x)$", (0,2.5), N); dot("$(-1,0)$", (-1,0), SE, fontsize(10)); dot("$(1,0)$", (1,0), SW, fontsize(10)); dot("$(0,2)$", (0,2), NE, fontsize(10)); [/asy]