Question

Sketch a graph of the polynomial function f(x) = x3 + 4x2 + 3x. Use it to complete each statement.

f(x) is
on the intervals (–∞, –3) and (–1, 0).

Answer 1

f(x) is negative on the intervals (–∞, –3) and (–1, 0).

Reason: f(x)=x(x+1)(x+3). For x<−3 all three factors are negative, so the product is negative. For −1<x<0, x is negative while x+1 and x+3 are positive, so the product is negative. (The graph crosses the x-axis at −3, −1, and 0.)