MathDB
Cubic

Source:

January 5, 2009

Problem Statement

Part of the graph of f(x) \equal{} x^3 \plus{} bx^2 \plus{} cx \plus{} d is shown. What is b b? [asy]import graph; unitsize(1.5cm); defaultpen(linewidth(.8pt)+fontsize(8pt)); dotfactor=3;
real y(real x) { return (x-1)*(x+1)*(x-2); }
path bounds=(-1.5,-1)--(1.5,-1)--(1.5,2.5)--(-1.5,2.5)--cycle;
pair[] points={(-1,0),(0,2),(1,0)}; draw(bounds,white); draw(graph(y,-1.5,1.5)); drawline((0,0),(1,0)); drawline((0,0),(0,1)); dot(points); label("(āˆ’1,0)(-1,0)",(-1,0),SE); label("(1,0)(1,0)",(1,0),SW); label("(0,2)(0,2)",(0,2),NE);
clip(bounds);[/asy] (A)\minus{}\!4 \qquad (B)\minus{}\!2 \qquad (C)\ 0 \qquad (D)\ 2 \qquad (E)\ 4